Honors Algebra 2 ~ Spring 2014 Name 1 Unit 3: Quadratic Functions and Equations

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Honors Algebra 2 ~ Spring 2014 Name 1 Unit 3: Quadratic Functions and Equations"

Transcription

1 Honors Algebra ~ Spring Name Unit : Quadratic Functions and Equations NC Objectives Covered:. Define and compute with comple numbers. Operate with algebraic epressions (polnomial, rational, comple fractions) to solve problems. Use quadratic functions and inequalities to model and solve problems. a. Solve using graphs. b. Interpret the constants and coefficients in the contet of the problem. Da Date Lesson Assignment Tues. Feb. 5 Intro to Parabolas/Transformations Discover Education Activit(computer lab) Handout Packet p. Wed. Feb. 6 Summar of Transformations(notepacket p. ) Standard Form to Verte Form Verte Form to Standard Form, Applications Packet p. Thurs. Feb. 7 Quadratic Regression What do ou know about Factoring? Packet p. Fri. Feb. 8 Factoring: GCF, Grouping, Trinomials, Difference of Squares Packet p. 5 5 Monda March * Quiz on Sections Solving Quadratic Equations b Factoring Packet p. 6 6 Tues. March ACT Solving Quadratic Equations b Factoring and Graphing Packet p. 7 7 Wed. March 5 Review of Radicals Comple Numbers Brochure Project : Packet p. 8 EVEN 8 Thurs. March 6 Comple Numbers Solve b taking the square root Packet p. 9 #-7 odd, #-8 9 Fri. March 7 REVIEW Quiz on das 7-9 Work on Brochure Project Mon. March Complete the Square/Station Activit Packet p. Tues. March Discriminant Quadratic Formula Handout Wed. March Solving Quadratic Inequalities and Quadratic Sstems Packet p. &

2 Honors Algebra ~ Spring Name Thurs. March Review/Quadratic Applications Packet p. & 5 Fri. March Quadratic Functions TEST Packet p. 7 & 8 Finish Brochure Project Mon. March 7 BROCHURE PROJECT DUE!! Homework Grade: ******************************************************************* Homework Da Part : Identif the verte, the ais of smmetr, the maimum or minimum value, and the domain and range of each parabola. ) ) 5 ) Verte Verte Verte AOS: AOS: AOS: ma/min value ma/min value ma/min domain domain domain range range range Part : Describe how to transform the parent function to the graph of each function below. ) ( ) ) ( ) ) ( ) ) ( ) +5 5).5 + 6).( ) - Part

3 Honors Algebra ~ Spring Name Homework Da Write in Standard Form. Identif the verte and -intercept.. = ( ) +. = -( ) 6. = -( + ) 8. = ( 8) + 5. = -( + 7) 6. =.( 5.) + Determine whether the equations in each pair are equivalent. 7. = ( ) 7 8. = ( + ) + 8 = + = 6 + Match each equation with the correct statement. 9. = a. The verte is at (, ).. = ( ) + b. The -intercept is 5.. = ( 5) + c. The -intercept is.. = d. The verte is at (5, ).. The Galleria, in BCE Place in Toronto, has man beautiful parabolic arches. One of the arches can be modeled b the function = -.5( 6.8) + 6. The -ais represents the floor in the Galleria and the -ais represents the height above the floor. Distances are in meters. a. Write the function in standard form. b. What is the height of the arch at its center? c. The -intercept represents the lowest point at one side of the base of an arch. What is this height?. The height, h, of a baseball thrown off a bridge can be modeled b the equation h = -5(t ) + where the height is measured in meters and t is the time in seconds since the ball was thrown. a. How high was the ball thrown? b. How long did the ball take to reach its highest point?

4 Honors Algebra ~ Spring Name. A to rocket is shot upward from ground level. The table shows the height of the rocket at different times. Time(seconds) Height(feet) a. Find a quadratic model for this data. b. Use the model to estimate the height of the rocket after.5 seconds.. Suppose ou are tossing an apple up to a friend on a third-stor balcon. After t seconds, the height of the apple in feet is given b h 6t 8.t.96. Your friend catches the apple just as it reaches its highest point. How long does the apple take to reach our friend, and at what height above the ground does our friend catch it?. the barber s profit p each week depends on his charge c per haircut. It is modeled b the equation p c c 7. What price should he charge for the largest profit?. A skating ring manager finds that revenue R based on an hourl fee F for sakting is represented b the function R 8F F. What hourl fee will produce maimum revenues? 5. The path of a baseball after it has been hit is modeled b the function h. d d, where h is the height in feet of the baseball and d is the distance in feet the baseball is from home plate. What is the maimum height reached b the baseball? How far is the baseball from home plate when it reaches its maimum height? 6. A lighting fiture manufacturer has dail production costs of C.5n n 8, Where C is the total cost in dollars and n is the number of light fitures produced. How man fitures should be produced to ield a minimum cost? 7. Find a quadratic model for the data. Use 98 as ear. Price of First-Class Stamp Year Price(Cents) a. What is the quadratic model? b. Describe a reasonable domain and range for our model. (Hint: This is a real situation.) c. Predict when the cost of a stamp will be 5 cents. Is this valid? Wh or wh not?

5 Honors Algebra ~ Spring Name 5 Factoring Practice a a b + ab b k 8k z z c + c c k + k. a a + ad d. - 5 REVIEW: Part A: For each function, the verte of the function s graph is given. Find a and b.. a b 7; (, ). a b 5; (, ). a b 8; (, ). a b ; (,) Part B:. The equation for the motion of a projectile fired straight up at an initial velocit of 6 ft/s is h = 6t - 6t, where h is the height in feet and t is the time in seconds. Find the time the projectile needs to reach its highest point. How high it will go?

6 Honors Algebra ~ Spring Name 6 Factor each polnomial

7 Honors Algebra ~ Spring Name 7 Solving Quadratic Equations Solve each equation b factoring = =. n + 5 = n. 9z = z 5. 7 = 6. c = c w - 5w + 6 = 8. d + d + 5 = 9. 5v + 9v + 6 =. j + 6 = j. 6k = 5. m - 8m = 5m. 6e = 5e + 6e. 9 = 6p Solve each equation b graphing. Round each answer to two decimal places

8 Honors Algebra ~ Spring Name 8 Simplifing Epressions Containing Comple Numbers

9 Honors Algebra ~ Spring Name 9 Simplifing Epressions Containing Comple Numbers Continued Find the value of m and n for which equation is true. ) 8 5i m ni ) ( m n) ( m n) i 5 5i ) (m 5 n) ( m) i i ) ( n) ( m n) i 8 i Solving using square roots. 5) n 5 6) n 8 8 7) 8b 7 9 8) 85

10 Honors Algebra ~ Spring Name Completing the square: Homework da Solve each equation b completing the square. Give the eact answer.. a a. v 6v 65. p 6 p. n 8n r r 6. a a 8 7. m m k k 6. p p 6. m m. 7p 8p 5 Part : Find the value of k that would make the left side of each equation a perfect square trinomial.. k 5. k. k 6. 9 k 5. k 8 6. k

11 Honors Algebra ~ Spring Name Homework Da : Completing the square Solve each quadratic b completing the square. Give the eact answer Part : Solve b factoring, completing the square, or taking the square root ( )

12 Honors Algebra ~ Spring Name Quadratic Applications. A smoke jumper jumps from a plane that is 7 feet above the ground. The function = gives a jumper s height in feet after seconds. a. How long is the jumper in free fall if the parachute opens at ft? b. How long is the jumper in free fall if the parachute opens at 9 ft?. You want to epand the garden below b planting a border of flowers. The border will have the same width around the entire garden. The flowers ou bought will fill an area of 76 ft. How wide should the border be? ft 6 6. One side of a rectangular garden is d less than the other side. The area of the garden is 6 d. Find the dimensions of the garden.. An electronics compan has a new line of portable radios with CD plaers. Their research suggests that the dail sales s for the new product can be modeled b s = -p + p +, where p is the price of each unit. a. Find the verte of the function. b. What is the maimum dail sales total for the new product? c. What price should the compan charge to make this profit? 5. The shape of the Gatewa Arch in St. Louis is a catenar curve, which closel resembles a parabola. The function closel models the shape of the arch, where is the 5 height in feet and is the horizontal distance from the base of the left side of the arch in feet. a. Graph the function and find its verte. b. What is the maimum height of the arch? c. What is the width of the arch at the base?

13 Honors Algebra ~ Spring Name Graphing Quadratic Inequalities Solving Quadratic Inequalities Solve each inequalit. -- >. -+6 < z z 8. t < >

14 Honors Algebra ~ Spring Name. A ball is thrown straight up with an initial velocit of 56 feet per second. The height of the ball t seconds after it is thrown is given b the formula h(t) = 56t 6t. a. What is the height of the ball after second? b. What is its maimum height? c. After how man seconds will it return to the ground? d. When will the ball be 5 feet above the ground?. An object is thrown upward into the air with an initial velocit of 8 feet per second. The formula h(t) = 8t 6t gives its height above the ground after t seconds. a. What is the height after seconds? b. What is the maimum height reached? c. For how man seconds will the object be in the air?. A baseball is projected upward from the top of a 8 foot tall building with an initial velocit of 8 feet per second. The distance s of the baseball from the ground at an time t, in seconds, is given b the equation s = -6t + 8t + 8. a. Find the time it takes for the baseball to strike the ground. b. What is the baseball s maimum height?. A rocket is shot upward such that it s height in feet, h, is given as h = 6t 5t, where t is the number of seconds since liftoff. a. Approimate the length of time the rocket is above feet. b. When will the rocket hit the ground? Use the formula h( t ) vt 6t where h(t) is the height of an object in feet, v is the object's initial velocit in feet per second, and t is the time in seconds. 5. An arrow is shot upward with a velocit of 6 feet per second. Ignoring the height of the archer, how long after the arrow is released does it hit the ground? 6. A tennis ball is hit upward with a velocit of 8 feet per second. Ignoring the height of the tennis plaer, how long does it take for the ball to fall to the ground?

15 Honors Algebra ~ Spring Name 5 Review Sheet: Unit. The following function represents the height, h, of a rocket t seconds after it is launched: h = - (t.5) +. When does the rocket reach its maimum height?. Bob wants to fence in his backard using his house as one side of the fence. He has 5 ft of fencing available. Find the dimensions of the fence needed to maimize the area.. The function h = -6t + 5t + represents the height of a ball t seconds after it is thrown. Could it hit a kite fling feet in the air?. A ball is thrown up in the air with an initial velocit of 56 feet per second. The height of the ball t seconds after it is thrown is given b the formula h(t) = 56t 6t. What is the maimum height of the ball? When does it return to the ground? 5. Solve 7 - > 6. Solve Solve using an method: + = 8. Solve using an method = 9. State the discriminant and nature of roots: - 7. State the discriminant and nature of roots: -. Solve: 8. Simplif: ( 5 i) ( i) (5 6 i ). Simplif: i 9 i. Simplif: 5. Simplif: ( 5 i)( 6 i ) 6. Simplif: ( i ) 7. Simplif: 7 i i 8. A rectangular garden contains ft and has a walk of uniform width surrounding it. If the entire area, including the walk, is ft ft., how wide is the sidewalk? Factor Completel: 9) a a a ) ) m m 6 ) m m 7 ) 6 Find the verte and ais of smmetr: ) 7 5) 7 6) ( ) 7) Write the equation of a parabola that has a verte at the origin and passes through the point (, -6). 8) Write the equation of a parabola that has a verte at (, -7), and passes through (,-9). 9) Describe how the parabola ( ) is shifted/different from.

16 Honors Algebra ~ Spring Name 6 Answers to Review Sheet. Ma at.5 sec.. dimensions: 87.5 ft 75 ft. no (graphs do not intersect). Ma height: 9 ft., and returns to the ground after.5 seconds 5. 5 or and 8. 5 i 9. discriminant = -8, so imaginar roots. discriminant =, so real rational root. i. 6-i i. 8. i i 6. 6i 7. 7 i 8. foot 9. ( a )( a ). 8( )( ). (m+)(m-). (m-)(m+7). ( )( )( ). V=(, ); a of s: = 5. V=(.75, -6.5); a of s: = V=(,); a of s: = ( ) 7 9. more narrow, left, up

17 Honors Algebra ~ Spring Name 7 Cumulative Review Units -. The attendance at a ball game was people. Student tickets cost $ and adult tickets cost $. $,5 was collected in ticket sales. Which sstem models the situation if s is the number of students and a is the number of a is the number of adults? A. s = a B. s = a C. s + a = D. s + a = (s + a) =,5,5(s + a) = s + a =,5 s + a =,5. What sstem describes this graph below? (tick marks are one unit apart) A. B. C. D.. Which of the following is FALSE? A. C. is the identit matri. B. D.. What is the solution of X has no inverse. is the identit matri for addition. 5? 6 A. 5 B. 5 C. 5 D. 5 E Which product does not eist? A. B. C. D Solve the formula for h. A ( b b ) h 7. A factor can produce products, and, with a profit of P = The Production of can eceed b no more than units. Also, production is limited b the Constraint. What production levels ield maimum profit? A. =, = B. =, = C. =, = D. =, = 6 8. What is the value of 7? A. B. 9 C. -9 D. -

18 Honors Algebra ~ Spring Name 8 a 6 6 b a 9. What are the values of a,b, and c if? 7 c 7 c A. a = -, b = 8, c = B. a = -, b =, c = C. a =, b = 8, c = - D. a = -, b =, c = -. What does z equal in the solution of the sstem z 8 z 7? z. What is the solution of in the sstem 6 5?. Write the equation of a line with slope 5 and passes through (, 9) in slope-intercept form.. For a campaign, a compan gave awa 5, tos to children. Tos and cost the compan $.9 and $.98, respectivel. The compan spent $5,6. How man of to did the give awa? A. 9 B., C., D.,. Two pickup trucks have capacities of ¼ and ½ ton. The made a total of 8 round trips to haul 7 ½ tons of crushed rock to a job site. Which matri equation could be used to determine how man round trips each truck made? A B. 5. The Coast Guard flies a rescue out of Elizabeth Cit to Hatteras in the middle of a Nor easter. It takes them one hour with a headwind to fl one hundred miles to get there and thirt minutes to fl back. How fast was the wind and how fast was the plane in still air? 6. What is the equation of the graph of an absolute function that opens down with verte (,) and passes Through the point (6,)? A. B. C. D. 7. Solve. A. B. C. or D. or 8. What is i ( i) ( i) written as a comple number in standard form? C D A. 6i B. 6i C. i D. i 9. Which quadratic function has a verte of (-,) and passes through the point (,9)? A. B. C. D Solve A. 6 B. 6 C. D.

MAT 1033C -- Martin-Gay Intermediate Algebra Chapter 8 (8.1, 8.2, 8.5, 8.6) Practice for the Exam

MAT 1033C -- Martin-Gay Intermediate Algebra Chapter 8 (8.1, 8.2, 8.5, 8.6) Practice for the Exam MAT 33C -- Martin-Ga Intermediate Algebra Chapter 8 (8.1 8. 8. 8.6) Practice for the Eam Name Date Da/Time: SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

More information

3.1 Graph Quadratic Functions

3.1 Graph Quadratic Functions 3. Graph Quadratic Functions in Standard Form Georgia Performance Standard(s) MMA3b, MMA3c Goal p Use intervals of increase and decrease to understand average rates of change of quadratic functions. Your

More information

Name Class Date. Quadratic Functions and Transformations. 4 6 x

Name Class Date. Quadratic Functions and Transformations. 4 6 x - Quadratic Functions and Transformations For Eercises, choose the correct letter.. What is the verte of the function 53()? D (, ) (, ) (, ) (, ). Which is the graph of the function f ()5(3) 5? F 6 6 O

More information

PRACTICE FINAL EXAM. 3. Solve: 3x 8 < 7. Write your answer using interval notation. Graph your solution on the number line.

PRACTICE FINAL EXAM. 3. Solve: 3x 8 < 7. Write your answer using interval notation. Graph your solution on the number line. MAC 1105 PRACTICE FINAL EXAM College Algebra *Note: this eam is provided as practice onl. It was based on a book previousl used for this course. You should not onl stud these problems in preparing for

More information

Mth 95 Module 4 Chapter 8 Spring Review - Solving quadratic equations using the quadratic formula

Mth 95 Module 4 Chapter 8 Spring Review - Solving quadratic equations using the quadratic formula Mth 95 Module 4 Chapter 8 Spring 04 Review - Solving quadratic equations using the quadratic formula Write the quadratic formula. The NUMBER of REAL and COMPLEX SOLUTIONS to a quadratic equation ( a b

More information

Copyrighted by Gabriel Tang B.Ed., B.Sc. Page 1.

Copyrighted by Gabriel Tang B.Ed., B.Sc. Page 1. Chapter : Linear and Quadratic Functions Chapter : Linear and Quadratic Functions -: Points and Lines Sstem of Linear Equations: - two or more linear equations on the same coordinate grid. Solution of

More information

Unit 2 Notes Packet on Quadratic Functions and Factoring

Unit 2 Notes Packet on Quadratic Functions and Factoring Name: Period: Unit Notes Packet on Quadratic Functions and Factoring Notes #: Graphing quadratic equations in standard form, verte form, and intercept form. A. Intro to Graphs of Quadratic Equations: a

More information

Mathematics 2201 Midterm Exam Review

Mathematics 2201 Midterm Exam Review Mathematics 0 Midterm Eam Review Chapter : Radicals Chapter 6: Quadratic Functions Chapter 7: Quadratic Equations. Evaluate: 6 8 (A) (B) (C) (D). Epress as an entire radical. (A) (B) (C) (D). What is the

More information

Quadratic Function. Parabola. Parent quadratic function. Vertex. Axis of Symmetry

Quadratic Function. Parabola. Parent quadratic function. Vertex. Axis of Symmetry Name: Chapter 10: Quadratic Equations and Functions Section 10.1: Graph = a + c Quadratic Function Parabola Parent quadratic function Verte Ais of Smmetr Parent Function = - -1 0 1 1 Eample 1: Make a table,

More information

Lesson 7.1 Polynomial Degree and Finite Differences

Lesson 7.1 Polynomial Degree and Finite Differences Lesson 7.1 Polnomial Degree and Finite Differences 1. Identif the degree of each polnomial. a. 1 b. 0. 1. 3. 3 c. 0 16 0. Determine which of the epressions are polnomials. For each polnomial, state its

More information

9 (0, 3) and solve equations to earn full credit.

9 (0, 3) and solve equations to earn full credit. Math 0 Intermediate Algebra II Final Eam Review Page of Instructions: (6, ) Use our own paper for the review questions. For the final eam, show all work on the eam. (-6, ) This is an algebra class do not

More information

5. Determine the discriminant for each and describe the nature of the roots.

5. Determine the discriminant for each and describe the nature of the roots. 4. Quadratic Equations Notes Day 1 1. Solve by factoring: a. 3 16 1 b. 3 c. 8 0 d. 9 18 0. Quadratic Formula: The roots of a quadratic equation of the form A + B + C = 0 with a 0 are given by the following

More information

Lesson 9.1 Using the Distance Formula

Lesson 9.1 Using the Distance Formula Lesson. Using the Distance Formula. Find the eact distance between each pair of points. a. (0, 0) and (, ) b. (0, 0) and (7, ) c. (, 8) and (, ) d. (, ) and (, 7) e. (, 7) and (8, ) f. (8, ) and (, 0)

More information

Shape and Structure. Forms of Quadratic Functions. Lesson 2.1 Assignment

Shape and Structure. Forms of Quadratic Functions. Lesson 2.1 Assignment Lesson.1 Assignment Name Date Shape and Structure Forms of Quadratic Functions 1. Analze the graph of the quadratic function. a. The standard form of a quadratic function is f() 5 a 1 b 1 c. What possible

More information

Mathematics 2201 Midterm Exam Review

Mathematics 2201 Midterm Exam Review Mathematics 0 Midterm Eam Review Chapter : Radicals Chapter : Quadratic Functions Chapter 7: Quadratic Equations. Evaluate: 8 (A) (B) (C) (D). Epress as an entire radical. (A) (B) (C) (D). What is the

More information

Properties of the Graph of a Quadratic Function. has a vertex with an x-coordinate of 2 b } 2a

Properties of the Graph of a Quadratic Function. has a vertex with an x-coordinate of 2 b } 2a 0.2 Graph 5 a 2 b c Before You graphed simple quadratic functions. Now You will graph general quadratic functions. Wh? So ou can investigate a cable s height, as in Eample 4. Ke Vocabular minimum value

More information

MATH College Algebra Review for Test 2

MATH College Algebra Review for Test 2 MATH 4 - College Algebra Review for Test Sections. and.. For f (x) = x + 4x + 5, give (a) the x-intercept(s), (b) the -intercept, (c) both coordinates of the vertex, and (d) the equation of the axis of

More information

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Spring 0 Math 08 Eam Preparation Ch Dressler Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the quadratic equation b the square root propert.

More information

5. 2. The solution set is 7 6 i, 7 x. Since b = 20, add

5. 2. The solution set is 7 6 i, 7 x. Since b = 20, add Chapter : Quadratic Equations and Functions Chapter Review Eercises... 5 8 6 8 The solution set is 8, 8. 5 5 5 5 5 5 The solution set is 5,5. Rationalize the denominator. 6 The solution set is. 8 8 9 6

More information

Chapters 8 & 9 Review for Final

Chapters 8 & 9 Review for Final Math 203 - Intermediate Algebra Professor Valdez Chapters 8 & 9 Review for Final SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the formula for

More information

Final Exam Review Part 2 #4

Final Exam Review Part 2 #4 Final Eam Review Part # Intermediate Algebra / MAT 135 Fall 01 Master (Prof. Fleischner) Student Name/ID: 1. Solve for, where is a real number. + = 8. Solve for, where is a real number. 9 1 = 3. Solve

More information

SECTION 3.1: Quadratic Functions

SECTION 3.1: Quadratic Functions SECTION 3.: Quadratic Functions Objectives Graph and Analyze Quadratic Functions in Standard and Verte Form Identify the Verte, Ais of Symmetry, and Intercepts of a Quadratic Function Find the Maimum or

More information

HAlgebra 2: Unit 7: Chapter 9 Spring Day Date Lesson Assignment. Section 9.1: Direct, Inverse, & Joint Variation Classwork: Packet p.

HAlgebra 2: Unit 7: Chapter 9 Spring Day Date Lesson Assignment. Section 9.1: Direct, Inverse, & Joint Variation Classwork: Packet p. HAlgebra : Unit 7: Chapter Spring 0 Name RATIONAL FUNCTIONS. NC Objectives:.0 Operate with algebraic epressions (polynomial, rational, comple fractions) to solve problems..0 Model and solve problems using

More information

Chapter 5: Quadratic Equations and Functions 5.1 Modeling Data With Quadratic Functions Quadratic Functions and Their Graphs

Chapter 5: Quadratic Equations and Functions 5.1 Modeling Data With Quadratic Functions Quadratic Functions and Their Graphs Ch 5 Alg Note Sheet Ke Chapter 5: Quadratic Equations and Functions 5.1 Modeling Data With Quadratic Functions Quadratic Functions and Their Graphs Definition: Standard Form of a Quadratic Function The

More information

Nonlinear Systems. No solution One solution Two solutions. Solve the system by graphing. Check your answer.

Nonlinear Systems. No solution One solution Two solutions. Solve the system by graphing. Check your answer. 8-10 Nonlinear Sstems CC.9-1.A.REI.7 Solve a simple sstem consisting of a linear equation and a quadratic equation in two variables algebraicall and graphicall. Objective Solve sstems of equations in two

More information

4 B. 4 D. 4 F. 3. How can you use the graph of a quadratic equation to determine the number of real solutions of the equation?

4 B. 4 D. 4 F. 3. How can you use the graph of a quadratic equation to determine the number of real solutions of the equation? 3.1 Solving Quadratic Equations COMMON CORE Learning Standards HSA-SSE.A. HSA-REI.B.b HSF-IF.C.8a Essential Question Essential Question How can ou use the graph of a quadratic equation to determine the

More information

Lesson Master 9-1B. REPRESENTATIONS Objective G. Questions on SPUR Objectives. 1. Let f(x) = 1. a. What are the coordinates of the vertex?

Lesson Master 9-1B. REPRESENTATIONS Objective G. Questions on SPUR Objectives. 1. Let f(x) = 1. a. What are the coordinates of the vertex? Back to Lesson 9-9-B REPRESENTATIONS Objective G. Let f() =. a. What are the coordinates of the verte? b. Is the verte a minimum or a maimum? c. Complete the table of values below. 3 0 3 f() d. Graph the

More information

Algebra II Notes Unit Six: Polynomials Syllabus Objectives: 6.2 The student will simplify polynomial expressions.

Algebra II Notes Unit Six: Polynomials Syllabus Objectives: 6.2 The student will simplify polynomial expressions. Algebra II Notes Unit Si: Polnomials Sllabus Objectives: 6. The student will simplif polnomial epressions. Review: Properties of Eponents (Allow students to come up with these on their own.) Let a and

More information

2.1 Evaluate and Graph Polynomial

2.1 Evaluate and Graph Polynomial 2. Evaluate and Graph Polnomial Functions Georgia Performance Standard(s) MM3Ab, MM3Ac, MM3Ad Your Notes Goal p Evaluate and graph polnomial functions. VOCABULARY Polnomial Polnomial function Degree of

More information

Quadratic Functions and Equations

Quadratic Functions and Equations Quadratic Functions and Equations Quadratic Graphs and Their Properties Objective: To graph quadratic functions of the form y = ax 2 and y = ax 2 + c. Objectives I can identify a vertex. I can grapy y

More information

M122 College Algebra Review for Final Exam

M122 College Algebra Review for Final Exam M1 College Algebra Review for Final Eam Revised Fall 017 for College Algebra - Beecher All answers should include our work (this could be a written eplanation of the result, a graph with the relevant feature

More information

Instructor: Imelda Valencia Course: A3 Honors Pre Calculus

Instructor: Imelda Valencia Course: A3 Honors Pre Calculus Student: Date: Instructor: Imelda Valencia Course: A3 Honors Pre Calculus 01 017 Assignment: Summer Homework for those who will be taking FOCA 017 01 onl available until Sept. 15 1. Write the epression

More information

MATH 115: Final Exam Review. Can you find the distance between two points and the midpoint of a line segment? (1.1)

MATH 115: Final Exam Review. Can you find the distance between two points and the midpoint of a line segment? (1.1) MATH : Final Eam Review Can ou find the distance between two points and the midpoint of a line segment? (.) () Consider the points A (,) and ( 6, ) B. (a) Find the distance between A and B. (b) Find the

More information

Find the distance between the pair of points. 2) (7, -7) and (3, -5) A) 12 3 units B) 2 5 units C) 6 units D) 12 units B) 8 C) 63 2

Find the distance between the pair of points. 2) (7, -7) and (3, -5) A) 12 3 units B) 2 5 units C) 6 units D) 12 units B) 8 C) 63 2 Sample Departmental Final - Math 9 Write the first five terms of the sequence whose general term is given. 1) a n = n 2 - n 0, 2,, 12, 20 B) 2,, 12, 20, 30 C) 0, 3, 8, 1, 2 D) 1,, 9, 1, 2 Find the distance

More information

Write Quadratic Functions and Models

Write Quadratic Functions and Models 4.0 A..B, A.6.B, A.6.C, A.8.A TEKS Write Quadratic Functions and Models Before You wrote linear functions and models. Now You will write quadratic functions and models. Wh? So ou can model the cross section

More information

Algebra II 5.3 Solving Quadratic Equations by Finding Square Roots

Algebra II 5.3 Solving Quadratic Equations by Finding Square Roots 5.3 Solving Quadratic Equations by Finding Square Roots Today I am solving quadratic equations by finding square roots. I am successful today when solve quadratic functions using square roots. It is important

More information

25) x x + 30 x2 + 15x ) x Graph the equation. 30) y = - x - 1

25) x x + 30 x2 + 15x ) x Graph the equation. 30) y = - x - 1 Pre-AP Algebra Final Eam Review Solve. ) A stone is dropped from a tower that is feet high. The formula h = - t describes the stoneʹs height above the ground, h, in feet, t seconds after it was dropped.

More information

2.3 Quadratic Functions

2.3 Quadratic Functions 88 Linear and Quadratic Functions. Quadratic Functions You ma recall studing quadratic equations in Intermediate Algebra. In this section, we review those equations in the contet of our net famil of functions:

More information

Answer Explanations. The SAT Subject Tests. Mathematics Level 1 & 2 TO PRACTICE QUESTIONS FROM THE SAT SUBJECT TESTS STUDENT GUIDE

Answer Explanations. The SAT Subject Tests. Mathematics Level 1 & 2 TO PRACTICE QUESTIONS FROM THE SAT SUBJECT TESTS STUDENT GUIDE The SAT Subject Tests Answer Eplanations TO PRACTICE QUESTIONS FROM THE SAT SUBJECT TESTS STUDENT GUIDE Mathematics Level & Visit sat.org/stpractice to get more practice and stud tips for the Subject Test

More information

Graphing Calculator Computations 2

Graphing Calculator Computations 2 Graphing Calculator Computations A) Write the graphing calculator notation and B) Evaluate each epression. 4 1) 15 43 8 e) 15 - -4 * 3^ + 8 ^ 4/ - 1) ) 5 ) 8 3 3) 3 4 1 8 3) 7 9 4) 1 3 5 4) 5) 5 5) 6)

More information

Study Guide and Intervention. The Quadratic Formula and the Discriminant. Quadratic Formula. Replace a with 1, b with -5, and c with -14.

Study Guide and Intervention. The Quadratic Formula and the Discriminant. Quadratic Formula. Replace a with 1, b with -5, and c with -14. Study Guide and Intervention Quadratic Formula The Quadratic Formula can be used to solve any quadratic equation once it is written in the form a 2 + b + c = 0. Quadratic Formula The solutions of a 2 +

More information

Objectives To solve quadratic equations using the quadratic formula To find the number of solutions of a quadratic equation

Objectives To solve quadratic equations using the quadratic formula To find the number of solutions of a quadratic equation 9-6 The Quadratic Formula and the Discriminant Content Standards A.REI..a Use the method of completing the square to transform an quadratic equation in into an equation of the form ( p) 5 q... Derive the

More information

Law of Sines, Law of Cosines, Heron s Formula:

Law of Sines, Law of Cosines, Heron s Formula: PreAP Math Analsis nd Semester Review Law of Sines, Law of Cosines, Heron s Formula:. Determine how man solutions the triangle has and eplain our reasoning. (FIND YOUR FLOW CHART) a. A = 4, a = 4 ards,

More information

State whether the following statements are true or false: 27.

State whether the following statements are true or false: 27. Cumulative MTE -9 Review This packet includes major developmental math concepts that students ma use to prepare for the VPT Math (Virginia Placement Test for Math or for students to use to review essential

More information

State whether the following statements are true or false: 30. 1

State whether the following statements are true or false: 30. 1 Cumulative MTE -9 Review This packet includes major developmental math concepts that students ma use to prepare for the VPT Math (Virginia Placement Test for Math or for students to use to review essential

More information

6.3 Interpreting Vertex Form and Standard Form

6.3 Interpreting Vertex Form and Standard Form Name Class Date 6.3 Interpreting Verte Form and Standard Form Essential Question: How can ou change the verte form of a quadratic function to standard form? Resource Locker Eplore Identifing Quadratic

More information

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Practice for the Final Eam MAC 1 Sullivan Version 1 (2007) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the distance d(p1, P2) between the points

More information

Quadratic Equations and Complex Numbers

Quadratic Equations and Complex Numbers Quadratic Equations and Comple Numbers.1 Solving Quadratic Equations. Comple Numbers.3 Completing the Square. Using the Quadratic Formula.5 Solving Nonlinear Sstems. Quadratic Inequalities Robot-Building

More information

= x. Algebra II Notes Quadratic Functions Unit Graphing Quadratic Functions. Math Background

= x. Algebra II Notes Quadratic Functions Unit Graphing Quadratic Functions. Math Background Algebra II Notes Quadratic Functions Unit 3.1 3. Graphing Quadratic Functions Math Background Previousl, ou Identified and graphed linear functions Applied transformations to parent functions Graphed quadratic

More information

Assessment Readiness. 28 Unit 1 MIXED REVIEW. 1. Look at each number. Is the number between 2π and

Assessment Readiness. 28 Unit 1 MIXED REVIEW. 1. Look at each number. Is the number between 2π and MODULE 1 1. Look at each number. Is the number between π and 5? Select or for epressions A C. A. 6 _ 3 5π B. C. 3 5. Consider the number - 11 15. A. The number is rational. True False B. The number can

More information

AP Calculus BC Summer Review

AP Calculus BC Summer Review AP Calculus BC 07-08 Summer Review Due September, 07 Name: All students entering AP Calculus BC are epected to be proficient in Pre-Calculus skills. To enhance your chances for success in this class, it

More information

One of the most common applications of Calculus involves determining maximum or minimum values.

One of the most common applications of Calculus involves determining maximum or minimum values. 8 LESSON 5- MAX/MIN APPLICATIONS (OPTIMIZATION) One of the most common applications of Calculus involves determining maimum or minimum values. Procedure:. Choose variables and/or draw a labeled figure..

More information

Find the integral. 12) 15)

Find the integral. 12) 15) Find the location of the indicated absolute etremum within the specified domain. ) Minimum of f() = /- /; [0, ] 8) Maimum h() ) Minimum of f() = - + - ; [-, ] ) Minimum of f() = ( + )/; [-, ] ) Maimum

More information

Chapter 3: Polynomial and Rational Functions

Chapter 3: Polynomial and Rational Functions Chapter 3: Polynomial and Rational Functions Section 3.1 Power Functions & Polynomial Functions... 155 Section 3. Quadratic Functions... 163 Section 3.3 Graphs of Polynomial Functions... 176 Section 3.4

More information

Quadratic Equations Chapter Questions

Quadratic Equations Chapter Questions Quadratic Equations Chapter Questions 1. Describe the characteristics of a quadratic equation. 2. What are the steps for graphing a quadratic function? 3. How can you determine the number of solutions

More information

CHAPTER 1 Functions, Graphs, and Limits

CHAPTER 1 Functions, Graphs, and Limits CHAPTER Functions, Graphs, and Limits Section. The Cartesian Plane and the Distance Formula... Section. Graphs of Equations...8 Section. Lines in the Plane and Slope... Mid-Chapter Quiz Solutions... Section.

More information

LESSON #11 - FORMS OF A LINE COMMON CORE ALGEBRA II

LESSON #11 - FORMS OF A LINE COMMON CORE ALGEBRA II LESSON # - FORMS OF A LINE COMMON CORE ALGEBRA II Linear functions come in a variet of forms. The two shown below have been introduced in Common Core Algebra I and Common Core Geometr. TWO COMMON FORMS

More information

8.2 Solving Quadratic Equations by the Quadratic Formula

8.2 Solving Quadratic Equations by the Quadratic Formula Section 8. Solving Quadratic Equations by the Quadratic Formula 85 8. Solving Quadratic Equations by the Quadratic Formula S Solve Quadratic Equations by Using the Quadratic Formula. Determine the Number

More information

Skills Practice Skills Practice for Lesson 1.1

Skills Practice Skills Practice for Lesson 1.1 Skills Practice Skills Practice for Lesson. Name Date Lots and Projectiles Introduction to Quadratic Functions Vocabular Give an eample of each term.. quadratic function 9 0. vertical motion equation s

More information

Working with Quadratic Functions: Standard and Factored Forms

Working with Quadratic Functions: Standard and Factored Forms 14 Chapter 3 Working with Quadratic Functions: Standard and Factored Forms GOALS You will be able to Epand and simplify quadratic epressions, solve quadratic equations, and relate the roots of a quadratic

More information

Using Intercept Form

Using Intercept Form 8.5 Using Intercept Form Essential Question What are some of the characteristics of the graph of f () = a( p)( q)? Using Zeros to Write Functions Work with a partner. Each graph represents a function of

More information

Chapter 4. Chapter 4 Opener. Section 4.1. Big Ideas Math Blue Worked-Out Solutions. x 2. Try It Yourself (p. 147) x 0 1. y ( ) x 2

Chapter 4. Chapter 4 Opener. Section 4.1. Big Ideas Math Blue Worked-Out Solutions. x 2. Try It Yourself (p. 147) x 0 1. y ( ) x 2 Chapter Chapter Opener Tr It Yourself (p. 7). As the input decreases b, the output increases b.. Input As the input increases b, the output increases b.. As the input decreases b, the output decreases

More information

C)not a function. B) function domain: {-3, 2, 4, 6} range: {-7, 4, 2, -1}

C)not a function. B) function domain: {-3, 2, 4, 6} range: {-7, 4, 2, -1} Name Spring Semester Final Review (Dual) Precalculus MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the relation represents a function.

More information

Unit 11 - Solving Quadratic Functions PART TWO

Unit 11 - Solving Quadratic Functions PART TWO Unit 11 - Solving Quadratic Functions PART TWO PREREQUISITE SKILLS: students should be able to add, subtract and multiply polynomials students should be able to factor polynomials students should be able

More information

16x y 8x. 16x 81. U n i t 3 P t 1 H o n o r s P a g e 1. Math 3 Unit 3 Day 1 - Factoring Review. I. Greatest Common Factor GCF.

16x y 8x. 16x 81. U n i t 3 P t 1 H o n o r s P a g e 1. Math 3 Unit 3 Day 1 - Factoring Review. I. Greatest Common Factor GCF. P a g e 1 Math 3 Unit 3 Day 1 - Factoring Review I. Greatest Common Factor GCF Eamples: A. 3 6 B. 4 8 4 C. 16 y 8 II. Difference of Two Squares Draw ( - ) ( + ) Square Root 1 st and Last Term Eamples:

More information

y x+ 2. A rectangular frame for a painting has a perimeter of 82 inches. If the length of the frame is 25 inches, find the width of the frame.

y x+ 2. A rectangular frame for a painting has a perimeter of 82 inches. If the length of the frame is 25 inches, find the width of the frame. . Simplif the complex fraction x 4 4 x. x 4 x x 4 x x 4 x x 4 x x E) 4 x. A rectangular frame for a painting has a perimeter of 8 inches. If the length of the frame is inches, find the width of the frame.

More information

Precalculus Fall Final Exam REVIEW Evaluate the function at the specified value(s) of the independent variable and simplify.

Precalculus Fall Final Exam REVIEW Evaluate the function at the specified value(s) of the independent variable and simplify. Precalculus Fall Final Eam EVIEW 016-017 1. Model the following situation with a linear equation in slope-intercept form. 4 The gas tank in a truck holds 15 gallons. The truck uses gallon per mile. 7.

More information

Math 2412 Pre Calculus TEST 2 Prep Fall 2011

Math 2412 Pre Calculus TEST 2 Prep Fall 2011 Math 41 Pre Calculus TEST Prep Fall 011 Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the eact value under the given conditions. 1) sin α

More information

3.1. Shape and Structure Forms of Quadratic Functions ESSENTIAL IDEAS TEXAS ESSENTIAL KNOWLEDGE AND SKILLS FOR MATHEMATICS 169A

3.1. Shape and Structure Forms of Quadratic Functions ESSENTIAL IDEAS TEXAS ESSENTIAL KNOWLEDGE AND SKILLS FOR MATHEMATICS 169A Shape and Structure Forms of Quadratic Functions.1 LEARNING GOALS KEY TERMS In this lesson, ou will: Match a quadratic function with its corresponding graph. Identif ke characteristics of quadratic functions

More information

Section 3.1 Power Functions & Polynomial Functions

Section 3.1 Power Functions & Polynomial Functions Chapter : Polynomial and Rational Functions Section. Power Functions & Polynomial Functions... 59 Section. Quadratic Functions... 67 Section. Graphs of Polynomial Functions... 8 Section.4 Factor Theorem

More information

Lesson 7.1 Polynomial Degree and Finite Differences

Lesson 7.1 Polynomial Degree and Finite Differences Lesson 7.1 Polynomial Degree and Finite Differences 1. Identify the degree of each polynomial. a. 1 b. 0.2 1. 2 3.2 3 c. 20 16 2 20 2. Determine which of the epressions are polynomials. For each polynomial,

More information

LESSON #17 - FACTORING COMMON CORE ALGEBRA II FACTOR TWO IMPORTANT MEANINGS

LESSON #17 - FACTORING COMMON CORE ALGEBRA II FACTOR TWO IMPORTANT MEANINGS 1 LESSON #17 - FACTORING COMMON CORE ALGEBRA II In the study of algebra there are certain skills that are called gateway skills because without them a student simply cannot enter into many more comple

More information

Linear and Nonlinear Systems of Equations. The Method of Substitution. Equation 1 Equation 2. Check (2, 1) in Equation 1 and Equation 2: 2x y 5?

Linear and Nonlinear Systems of Equations. The Method of Substitution. Equation 1 Equation 2. Check (2, 1) in Equation 1 and Equation 2: 2x y 5? 3330_070.qd 96 /5/05 Chapter 7 7. 9:39 AM Page 96 Sstems of Equations and Inequalities Linear and Nonlinear Sstems of Equations What ou should learn Use the method of substitution to solve sstems of linear

More information

Solving Quadratic Equations

Solving Quadratic Equations 9 Solving Quadratic Equations 9. Properties of Radicals 9. Solving Quadratic Equations b Graphing 9. Solving Quadratic Equations Using Square Roots 9. Solving Quadratic Equations b Completing the Square

More information

Math 2 1. Lesson 4-5: Completing the Square. When a=1 in a perfect square trinomial, then. On your own: a. x 2 18x + = b.

Math 2 1. Lesson 4-5: Completing the Square. When a=1 in a perfect square trinomial, then. On your own: a. x 2 18x + = b. Math 1 Lesson 4-5: Completing the Square Targets: I can identify and complete perfect square trinomials. I can solve quadratic equations by Completing the Square. When a=1 in a perfect square trinomial,

More information

SAMPLE. Chapter 1: Basic Skills. Chapter 2: Systems of Linear Equations. Chapter 3: Analytic Geometry. Chapter 4: Polynomials

SAMPLE. Chapter 1: Basic Skills. Chapter 2: Systems of Linear Equations. Chapter 3: Analytic Geometry. Chapter 4: Polynomials Overview... 3 Chapter : Basic Skills. Order of Operations... 6. lgebraic Epressions... 9.3 Equations.... Simple Linear Equations... 5 Chapter : Sstems of Linear Equations. Graphing Sstems of Linear Equations....

More information

LESSON #12 - FORMS OF A LINE COMMON CORE ALGEBRA II

LESSON #12 - FORMS OF A LINE COMMON CORE ALGEBRA II LESSON # - FORMS OF A LINE COMMON CORE ALGEBRA II Linear functions come in a variet of forms. The two shown below have been introduced in Common Core Algebra I and Common Core Geometr. TWO COMMON FORMS

More information

Lesson 10.1 Solving Quadratic Equations

Lesson 10.1 Solving Quadratic Equations Lesson 10.1 Solving Quadratic Equations 1. Sketch the graph of a quadratic equation with each set of conditions. a. One -intercept and all nonnegative y-values b. The verte in the third quadrant and no

More information

Quadratic Equations - Square Root Property, Intro YouTube Video

Quadratic Equations - Square Root Property, Intro YouTube Video Quadratic Equations - Square Root Property, Intro YouTube Video 4 81 8 Section 8.1 = or = = or = = or = Solve: 144 36 7 54 1 Quadratic Equations - Square Root Property YouTube Video Isolate the Square

More information

Summary, Review, and Test

Summary, Review, and Test 45 Chapter Equations and Inequalities Chapter Summar Summar, Review, and Test DEFINITIONS AND CONCEPTS EXAMPLES. Eponential Functions a. The eponential function with base b is defined b f = b, where b

More information

Name: Period: SM Starter on Reading Quadratic Graph. This graph and equation represent the path of an object being thrown.

Name: Period: SM Starter on Reading Quadratic Graph. This graph and equation represent the path of an object being thrown. SM Name: Period: 7.5 Starter on Reading Quadratic Graph This graph and equation represent the path of an object being thrown. 1. What is the -ais measuring?. What is the y-ais measuring? 3. What are the

More information

Math 102 Final Exam Review

Math 102 Final Exam Review . Compute f ( + h) f () h Math 0 Final Eam Review for each of the following functions. Simplify your answers. f () 4 + 5 f ( ) f () + f ( ). Find the domain of each of the following functions. f( ) g (

More information

Math 110 Final Exam Review Revised December 2015

Math 110 Final Exam Review Revised December 2015 Math 110 Final Exam Review Revised December 2015 Factor out the GCF from each polynomial. 1) 60x - 15 2) 7x 8 y + 42x 6 3) x 9 y 5 - x 9 y 4 + x 7 y 2 - x 6 y 2 Factor each four-term polynomial by grouping.

More information

Solving Quadratic Equations by Graphing 9.1. ACTIVITY: Solving a Quadratic Equation by Graphing. How can you use a graph to solve a quadratic

Solving Quadratic Equations by Graphing 9.1. ACTIVITY: Solving a Quadratic Equation by Graphing. How can you use a graph to solve a quadratic 9. Solving Quadratic Equations b Graphing equation in one variable? How can ou use a graph to solve a quadratic Earlier in the book, ou learned that the -intercept of the graph of = a + b variables is

More information

121D Practice Test #

121D Practice Test # D Practice Test # College Algebra / Math D GARAGE (Prof. Vasan) Student Name/ID:. Write the epression as a single logarithm. 5log 8 w + 5 log 8 3log 8 z. Solve for. log + 3 = log + 6 ALEKS D Practice Test

More information

Algebra Notes Quadratic Functions and Equations Unit 08

Algebra Notes Quadratic Functions and Equations Unit 08 Note: This Unit contains concepts that are separated for teacher use, but which must be integrated by the completion of the unit so students can make sense of choosing appropriate methods for solving quadratic

More information

TO THE STUDENT: To best prepare for Test 4, do all the problems on separate paper. The answers are given at the end of the review sheet.

TO THE STUDENT: To best prepare for Test 4, do all the problems on separate paper. The answers are given at the end of the review sheet. MATH TEST 4 REVIEW TO THE STUDENT: To best prepare for Test 4, do all the problems on separate paper. The answers are given at the end of the review sheet. PART NON-CALCULATOR DIRECTIONS: The problems

More information

Last modified Spring 2016

Last modified Spring 2016 Math 00 Final Review Questions In problems 6, perform the indicated operations and simplif if necessar.. 8 6 8. 7 6. ( i) ( 4 i) 4. (8 i). ( 9 i)( 7 i) 6. ( i)( i) In problems 7-, solve the following applications.

More information

290 Chapter 1 Functions and Graphs

290 Chapter 1 Functions and Graphs 90 Chapter Functions and Graphs 7. Studies show that teting while driving is as risk as driving with a 0.08 blood alcohol level, the standard for drunk driving. The bar graph shows the number of fatalities

More information

1. m = 3, P (3, 1) 2. m = 2, P ( 5, 8) 3. m = 1, P ( 7, 1) 4. m = m = 0, P (3, 117) 8. m = 2, P (0, 3)

1. m = 3, P (3, 1) 2. m = 2, P ( 5, 8) 3. m = 1, P ( 7, 1) 4. m = m = 0, P (3, 117) 8. m = 2, P (0, 3) . Linear Functions 69.. Eercises To see all of the help resources associated with this section, click OSttS Chapter. In Eercises - 0, find both the point-slope form and the slope-intercept form of the

More information

9.3 Using the Quadratic Formula to Solve Equations

9.3 Using the Quadratic Formula to Solve Equations Name Class Date 9.3 Using the Quadratic Formula to Solve Equations Essential Question: What is the quadratic formula, and how can you use it to solve quadratic equations? Resource Locker Explore Deriving

More information

Unit 5: Quadratic Functions

Unit 5: Quadratic Functions Unit 5: Quadratic Functions LESSON #2: THE PARABOLA APPLICATIONS AND WORD PROBLEMS INVERSE OF A QUADRATIC FUNCTION DO NOW: Review from Lesson #1 (a)using the graph shown to the right, determine the equation

More information

Chapter 6 Resource Masters

Chapter 6 Resource Masters Chapter 6 Resource Masters Consumable Workbooks Man of the worksheets contained in the Chapter Resource Masters booklets are available as consumable workbooks. Stud Guide and Intervention Workbook 0-07-8809-X

More information

Classwork #40: Final Review: Solving Equations, Word Problems, Linear Equations, Systems of Linear Equations

Classwork #40: Final Review: Solving Equations, Word Problems, Linear Equations, Systems of Linear Equations Classwork #0: Final Review: Solving Equations, Word Problems, Linear Equations, Sstems of Linear Equations Solving Equations: Isolate the variable! Things to watch for: when ou have parentheses the inequalit

More information

CHAPTER 3 Applications of Differentiation

CHAPTER 3 Applications of Differentiation CHAPTER Applications of Differentiation Section. Etrema on an Interval.............. 0 Section. Rolle s Theorem and the Mean Value Theorem. 07 Section. Increasing and Decreasing Functions and the First

More information

Chapter 1 Notes: Quadratic Functions

Chapter 1 Notes: Quadratic Functions 19 Chapter 1 Notes: Quadratic Functions (Textbook Lessons 1.1 1.2) Graphing Quadratic Function A function defined by an equation of the form, The graph is a U-shape called a. Standard Form Vertex Form

More information

Algebra 2 Unit 1 Practice

Algebra 2 Unit 1 Practice Algebra Unit Practice LESSON - Use this information for Items. Aaron has $ to rent a bike in the cit. It costs $ per hour to rent a bike. The additional fee for a helmet is $ for the entire ride.. Write

More information

Math 101 chapter six practice exam MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Math 101 chapter six practice exam MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Math 1 chapter si practice eam MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Which equation matches the given calculator-generated graph and description?

More information

Algebra I. Administered May 2014 RELEASED

Algebra I. Administered May 2014 RELEASED STAAR State of Teas Assessments of Academic Readiness Algebra I Administered Ma 0 RELEASED Copright 0, Teas Education Agenc. All rights reserved. Reproduction of all or portions of this work is prohibited

More information

PRECALCULUS FINAL EXAM REVIEW

PRECALCULUS FINAL EXAM REVIEW PRECALCULUS FINAL EXAM REVIEW Evaluate the function at the indicated value of. Round our result to three decimal places.. f () 4(5 ); 0.8. f () e ; 0.78 Use the graph of f to describe the transformation

More information