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

Size: px
Start display at page:

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

Transcription

1 SM Name: Period: 7.5 Starter on Reading Quadratic Graph This graph and equation represent the path of an object being thrown.

2 1. What is the -ais measuring?. What is the y-ais measuring? 3. What are the units of the -ais? 4. What are the units of the y-ais? 5. At 10 seconds, what is the height? 6. How long did it take to get to 304 feet high? 7. What is the maimum point? 8. What is the maimum height? 9. How long does it take to get to the maimum height? 10. Why are there no points when the -coordinates are negative? 11. What is the y-intercept? 1. In a complete sentence, eplain what the y-intercept represents on this graph. 13. Where do you see the y-intercept in the equation? 14. How long does it take for the object to hit the ground? 15. What math vocabulary word(s) does this point represent? 16. Pick a point on the graph, eplain in complete sentences what that point represents on this graph.

3 SM Date: Objective: Section: Steps for solving stories: 1. READ the story, write down the information needed and define a variable. Write an equation 3. Solve for variable 4. Check Tips for solving story problems: Identify what you know. What are you trying to find out? Draw a picture or diagram to help you visualize the situation. Carefully define your variables. Translate the words into symbols. Use appropriate units. Make sure your answer makes sense. Hints: Sum: + Difference: Product: Quotient: Words that tell you to look for the verte: maimum, minimum, highest, lowest, biggest, littlest, largest, smallest, maimize, minimize. EXAMPLES: 1. A ski club sells calendars to raise money. The profit, P, in dollars, from selling calendars is given by the P = 10. equation ( ) Sketch a graph of the situation. Label the aes clearly. How much profit will the club make from selling 50 calendars? How many calendars must be sold for the club to make $700? How many calendars must be sold to maimize profit? What is the maimum profit?

4 . A rock is thrown upward from the ground by the wheel of a truck. Its height in feet above the ground after t ht = 16t + 0 t. seconds is given by the function ( ) Draw a sketch of the graph representing the path of the rock. What does each ais represent? How long does it take the rock to reach its maimum height? What is the maimum height of the rock? How long will it take for the rock to return to the ground? 3. A penny is thrown upward from the observation deck on the 10 nd floor of the Empire State Building. It s height, h, in feet, after t seconds is given by the equation ht ( ) = 16t + 9t+ 150 What is the height of the observation deck? (In other words, how high is the penny at t = 0? ) How high is the penny after seconds? The Empire State Building has a lightning rod with a tip that is 1454 ft above the ground. Will the penny reach the top of the lightning rod? (Hint: Find the maimum height and see if it s larger or smaller than 1454 ft.) When will the penny be 1110 feet above the ground? How long will it take for the penny to hit the ground?

5 SM Date: Section: Objective: Writing Quadratic Functions Given Key Features If you know the verte and another point on the parabola, or the roots and another point on the parabola, you can figure out the equation of the parabola. Writing a Quadratic Equation when You Know the Verte and Another Point 1. Use. Substitute in 3. Substitute in 4. (Don t forget ) 5. Write your final answer Eamples: Write an equation for each parabola described below. 1,, 0, 1 a) Verte: passes through b) Verte: 1, 3, passes through 3,5 c)

6 Writing a Quadratic Equation when You Know the Roots and Another Point 1. Use. Substitute in 3. Substitute in 4. (Don t forget ) 5. Write your final answer Eamples: Write an equation for each parabola described below. a) Roots: 1,0 and 3,0, passes through,9 b) Roots: 4,0 and 8,0, passes through 0,16 c)

7 Date: Section: SM Objective: f = + 3. Review Eample: Solve ( ) Notice that each of these inequalities below involves the value of + 3, which is represented by the y- coordinate of the graph. In each case, we are trying to figure out what -values (-coordinates) make the inequality true. When trying to find where + 3 > 0, we are trying to figure out what -coordinates have a y-coordinate that is bigger than zero in other words, where is the graph above the -ais? a) + 3> 0 b) ( ) f = + 3 c) + 3< 0 d) + 3 0

8 Solving a Quadratic Inequality Using the Graph: If the inequality involves or, the -intercepts in the solution set ( or ). 4. If the inequality involves < or >, the -intercepts in the solution set ( or ). The solutions of The solutions of The solutions of The solutions of a + b + c > 0 are the -values for which the graph is the -ais. a + b + c 0 are the -values for which the graph is the -ais. a + b + c < 0 are the -values for which the graph is the -ais. a + b + c 0 are the -values for which the graph is the -ais. 5. Eamples: Solve each inequality and graph the solution set on a number line. Write answer in interval notation. a) ( 3)( + 1) 0 b) ( )( ) 7 5 < 0 c) + 5> 0 d) 4 1 0

9 e) 4< 0 f) g) 4+ 4> 0 h) i) 4+ 4< 0 j)

ALGEBRA II-GRAPHING QUADRATICS THE GRAPH OF A QUADRATIC FUNCTION

ALGEBRA II-GRAPHING QUADRATICS THE GRAPH OF A QUADRATIC FUNCTION ALGEBRA II-GRAPHING QUADRATICS THE GRAPH OF A QUADRATIC FUNCTION The Quadratic Equation is written as: ; this equation has a degree of. Where a, b and c are integer coefficients (where a 0) The graph of

More information

Secondary Math 2H Unit 3 Notes: Factoring and Solving Quadratics

Secondary Math 2H Unit 3 Notes: Factoring and Solving Quadratics Secondary Math H Unit 3 Notes: Factoring and Solving Quadratics 3.1 Factoring out the Greatest Common Factor (GCF) Factoring: The reverse of multiplying. It means figuring out what you would multiply together

More information

Section 7.1 Objective 1: Solve Quadratic Equations Using the Square Root Property Video Length 12:12

Section 7.1 Objective 1: Solve Quadratic Equations Using the Square Root Property Video Length 12:12 Section 7.1 Video Guide Solving Quadratic Equations by Completing the Square Objectives: 1. Solve Quadratic Equations Using the Square Root Property. Complete the Square in One Variable 3. Solve Quadratic

More information

Honors Math 2 Unit 1 Test #2 Review 1

Honors Math 2 Unit 1 Test #2 Review 1 Honors Math Unit 1 Test # Review 1 Test Review & Study Guide Modeling with Quadratics Show ALL work for credit! Use etra paper, if needed. Factor Completely: 1. Factor 8 15. Factor 11 4 3. Factor 1 4.

More information

Secondary Math 2 Honors Unit 4 Graphing Quadratic Functions

Secondary Math 2 Honors Unit 4 Graphing Quadratic Functions SMH Secondary Math Honors Unit 4 Graphing Quadratic Functions 4.0 Forms of Quadratic Functions Form: ( ) f = a + b + c, where a 0. There are no parentheses. f = 3 + 7 Eample: ( ) Form: f ( ) = a( p)( q),

More information

Exam 2 Review F15 O Brien. Exam 2 Review:

Exam 2 Review F15 O Brien. Exam 2 Review: Eam Review:.. Directions: Completely rework Eam and then work the following problems with your book notes and homework closed. You may have your graphing calculator and some blank paper. The idea is to

More information

Math 103 Final Exam Review Problems Rockville Campus Fall 2006

Math 103 Final Exam Review Problems Rockville Campus Fall 2006 Math Final Eam Review Problems Rockville Campus Fall. Define a. relation b. function. For each graph below, eplain why it is or is not a function. a. b. c. d.. Given + y = a. Find the -intercept. b. Find

More information

Learning Targets: Standard Form: Quadratic Function. Parabola. Vertex Max/Min. x-coordinate of vertex Axis of symmetry. y-intercept.

Learning Targets: Standard Form: Quadratic Function. Parabola. Vertex Max/Min. x-coordinate of vertex Axis of symmetry. y-intercept. Name: Hour: Algebra A Lesson:.1 Graphing Quadratic Functions Learning Targets: Term Picture/Formula In your own words: Quadratic Function Standard Form: Parabola Verte Ma/Min -coordinate of verte Ais of

More information

Algebra I Practice Questions ? 1. Which is equivalent to (A) (B) (C) (D) 2. Which is equivalent to 6 8? (A) 4 3

Algebra I Practice Questions ? 1. Which is equivalent to (A) (B) (C) (D) 2. Which is equivalent to 6 8? (A) 4 3 1. Which is equivalent to 64 100? 10 50 8 10 8 100. Which is equivalent to 6 8? 4 8 1 4. Which is equivalent to 7 6? 4 4 4. Which is equivalent to 4? 8 6 Page 1 of 0 11 Practice Questions 6 1 5. Which

More information

Graphs and Solutions for Quadratic Equations

Graphs and Solutions for Quadratic Equations Format y = a + b + c where a 0 Graphs and Solutions for Quadratic Equations Graphing a quadratic equation creates a parabola. If a is positive, the parabola opens up or is called a smiley face. If a is

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

Additional Factoring Examples:

Additional Factoring Examples: Honors Algebra -3 Solving Quadratic Equations by Graphing and Factoring Learning Targets 1. I can solve quadratic equations by graphing. I can solve quadratic equations by factoring 3. I can write a quadratic

More information

Lesson 4.1 Exercises, pages

Lesson 4.1 Exercises, pages Lesson 4.1 Eercises, pages 57 61 When approimating answers, round to the nearest tenth. A 4. Identify the y-intercept of the graph of each quadratic function. a) y = - 1 + 5-1 b) y = 3-14 + 5 Use mental

More information

Algebra II Honors Unit 3 Assessment Review Quadratic Functions. Formula Box. f ( x) 2 x 3 25 from the parent graph of

Algebra II Honors Unit 3 Assessment Review Quadratic Functions. Formula Box. f ( x) 2 x 3 25 from the parent graph of Name: Algebra II Honors Unit 3 Assessment Review Quadratic Functions Date: Formula Box x = b a x = b ± b 4ac a h 6t h 0 ) What are the solutions of x 3 5? x 8or x ) Describe the transformation of f ( x)

More information

SYSTEMS OF THREE EQUATIONS

SYSTEMS OF THREE EQUATIONS SYSTEMS OF THREE EQUATIONS 11.2.1 11.2.4 This section begins with students using technology to eplore graphing in three dimensions. By using strategies that they used for graphing in two dimensions, students

More information

ALGEBRA II SEMESTER EXAMS PRACTICE MATERIALS SEMESTER (1.2-1) What is the inverse of f ( x) 2x 9? (A) (B) x x (C) (D) 2. (1.

ALGEBRA II SEMESTER EXAMS PRACTICE MATERIALS SEMESTER (1.2-1) What is the inverse of f ( x) 2x 9? (A) (B) x x (C) (D) 2. (1. 04-05 SEMESTER EXAMS. (.-) What is the inverse of f ( ) 9? f f f f ( ) 9 ( ) 9 9 ( ) ( ) 9. (.-) If 4 f ( ) 8, what is f ( )? f( ) ( 8) 4 f ( ) 8 4 4 f( ) 6 4 f( ) ( 8). (.4-) Which statement must be true

More information

20.2 Connecting Intercepts and Linear Factors

20.2 Connecting Intercepts and Linear Factors Name Class Date 20.2 Connecting Intercepts and Linear Factors Essential Question: How are -intercepts of a quadratic function and its linear factors related? Resource Locker Eplore Connecting Factors and

More information

Algebra I Quadratics Practice Questions

Algebra I Quadratics Practice Questions 1. Which is equivalent to 64 100? 10 50 8 10 8 100. Which is equivalent to 6 8? 4 8 1 4. Which is equivalent to 7 6? 4 4 4. Which is equivalent to 4? 8 6 From CCSD CSE S Page 1 of 6 1 5. Which is equivalent

More information

IB Questionbank Mathematical Studies 3rd edition. Quadratics. 112 min 110 marks. y l

IB Questionbank Mathematical Studies 3rd edition. Quadratics. 112 min 110 marks. y l IB Questionbank Mathematical Studies 3rd edition Quadratics 112 min 110 marks 1. The following diagram shows a straight line l. 10 8 y l 6 4 2 0 0 1 2 3 4 5 6 (a) Find the equation of the line l. The line

More information

Graph Quadratic Functions in Standard Form

Graph Quadratic Functions in Standard Form TEKS 4. 2A.4.A, 2A.4.B, 2A.6.B, 2A.8.A Graph Quadratic Functions in Standard Form Before You graphed linear functions. Now You will graph quadratic functions. Wh? So ou can model sports revenue, as in

More information

Algebra II Midterm Exam Review Packet

Algebra II Midterm Exam Review Packet Algebra II Midterm Eam Review Packet Name: Hour: CHAPTER 1 Midterm Review Evaluate the power. 1.. 5 5. 6. 7 Find the value of each epression given the value of each variable. 5. 10 when 5 10 6. when 6

More information

Section 3.3 Graphs of Polynomial Functions

Section 3.3 Graphs of Polynomial Functions 3.3 Graphs of Polynomial Functions 179 Section 3.3 Graphs of Polynomial Functions In the previous section we eplored the short run behavior of quadratics, a special case of polynomials. In this section

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

Math 103 Intermediate Algebra Final Exam Review Practice Problems

Math 103 Intermediate Algebra Final Exam Review Practice Problems Math 10 Intermediate Algebra Final Eam Review Practice Problems The final eam covers Chapter, Chapter, Sections 4.1 4., Chapter 5, Sections 6.1-6.4, 6.6-6.7, Chapter 7, Chapter 8, and Chapter 9. The list

More information

Name Class Date. Understanding How to Graph g(x) = a(x - h ) 2 + k

Name Class Date. Understanding How to Graph g(x) = a(x - h ) 2 + k Name Class Date - Transforming Quadratic Functions Going Deeper Essential question: How can ou obtain the graph of g() = a( h ) + k from the graph of f () =? 1 F-BF..3 ENGAGE Understanding How to Graph

More information

CHAPTER 3 : QUADRARIC FUNCTIONS MODULE CONCEPT MAP Eercise 1 3. Recognizing the quadratic functions Graphs of quadratic functions 4 Eercis

CHAPTER 3 : QUADRARIC FUNCTIONS MODULE CONCEPT MAP Eercise 1 3. Recognizing the quadratic functions Graphs of quadratic functions 4 Eercis ADDITIONAL MATHEMATICS MODULE 5 QUADRATIC FUNCTIONS CHAPTER 3 : QUADRARIC FUNCTIONS MODULE 5 3.1 CONCEPT MAP Eercise 1 3. Recognizing the quadratic functions 3 3.3 Graphs of quadratic functions 4 Eercise

More information

4.1 Solving Systems of Equations Graphically. Draw pictures to represent the possible number of solutions that a linear-quadratic system can have:

4.1 Solving Systems of Equations Graphically. Draw pictures to represent the possible number of solutions that a linear-quadratic system can have: 4.1 Solving Systems of Equations Graphically Linear- Quadratic A Linear-Quadratic System of Equations is a linear equation and a quadratic equation involving the same two variables. The solution(s) to

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

Characteristics of Quadratic Functions

Characteristics of Quadratic Functions . Characteristics of Quadratic Functions Essential Question What tpe of smmetr does the graph of f() = a( h) + k have and how can ou describe this smmetr? Parabolas and Smmetr Work with a partner. a. Complete

More information

QUADRATIC FUNCTIONS. ( x 7)(5x 6) = 2. Exercises: 1 3x 5 Sum: 8. We ll expand it by using the distributive property; 9. Let s use the FOIL method;

QUADRATIC FUNCTIONS. ( x 7)(5x 6) = 2. Exercises: 1 3x 5 Sum: 8. We ll expand it by using the distributive property; 9. Let s use the FOIL method; QUADRATIC FUNCTIONS A. Eercises: 1.. 3. + = + = + + = +. ( 1)(3 5) (3 5) 1(3 5) 6 10 3 5 6 13 5 = = + = +. ( 7)(5 6) (5 6) 7(5 6) 5 6 35 4 5 41 4 3 5 6 10 1 3 5 Sum: 6 + 10+ 3 5 ( + 1)(3 5) = 6 + 13 5

More information

Mathematics 10 Page 1 of 7 The Quadratic Function (Vertex Form): Translations. and axis of symmetry is at x a.

Mathematics 10 Page 1 of 7 The Quadratic Function (Vertex Form): Translations. and axis of symmetry is at x a. Mathematics 10 Page 1 of 7 Verte form of Quadratic Relations The epression a p q defines a quadratic relation called the verte form with a horizontal translation of p units and vertical translation of

More information

Part 1: Integration problems from exams

Part 1: Integration problems from exams . Find each of the following. ( (a) 4t 4 t + t + (a ) (b ) Part : Integration problems from 4-5 eams ) ( sec tan sin + + e e ). (a) Let f() = e. On the graph of f pictured below, draw the approimating

More information

Mini-Lecture 8.1 Solving Quadratic Equations by Completing the Square

Mini-Lecture 8.1 Solving Quadratic Equations by Completing the Square Mini-Lecture 8.1 Solving Quadratic Equations b Completing the Square Learning Objectives: 1. Use the square root propert to solve quadratic equations.. Solve quadratic equations b completing the square.

More information

Mth Quadratic functions and quadratic equations

Mth Quadratic functions and quadratic equations Mth 0 - Quadratic functions and quadratic equations Name Find the product. 1) 8a3(2a3 + 2 + 12a) 2) ( + 4)( + 6) 3) (3p - 1)(9p2 + 3p + 1) 4) (32 + 4-4)(2-3 + 3) ) (4a - 7)2 Factor completel. 6) 92-4 7)

More information

Outline. 1 The Role of Functions. 2 Polynomial Functions. 3 Power Functions. 4 Rational Functions. 5 Exponential & Logarithmic Functions

Outline. 1 The Role of Functions. 2 Polynomial Functions. 3 Power Functions. 4 Rational Functions. 5 Exponential & Logarithmic Functions Outline MS11: IT Mathematics Functions Catalogue of Essential Functions John Carroll School of Mathematical Sciences Dublin City University 1 The Role of Functions 3 Power Functions 4 Rational Functions

More information

7.2 Connecting Intercepts and Linear Factors

7.2 Connecting Intercepts and Linear Factors Name Class Date 7.2 Connecting Intercepts and Linear Factors Essential Question: How are -intercepts of a quadratic function and its linear factors related? Resource Locker Eplore Connecting Factors and

More information

Name Class Date. Identify the vertex of each graph. Tell whether it is a minimum or a maximum.

Name Class Date. Identify the vertex of each graph. Tell whether it is a minimum or a maximum. Practice Quadratic Graphs and Their Properties Identify the verte of each graph. Tell whether it is a minimum or a maimum. 1. y 2. y 3. 2 4 2 4 2 2 y 4 2 2 2 4 Graph each function. 4. f () = 3 2 5. f ()

More information

Math 2412 Activity 2(Due by EOC Feb. 27) Find the quadratic function that satisfies the given conditions. Show your work!

Math 2412 Activity 2(Due by EOC Feb. 27) Find the quadratic function that satisfies the given conditions. Show your work! Math 4 Activity (Due by EOC Feb 7) Find the quadratic function that satisfies the given conditions Show your work! The graph has a verte at 5, and it passes through the point, 0 7 The graph passes through

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

Fair Game Review. Chapter 8. Graph the linear equation. Big Ideas Math Algebra Record and Practice Journal

Fair Game Review. Chapter 8. Graph the linear equation. Big Ideas Math Algebra Record and Practice Journal Name Date Chapter Graph the linear equation. Fair Game Review. =. = +. =. =. = +. = + Copright Big Ideas Learning, LLC Big Ideas Math Algebra Name Date Chapter Fair Game Review (continued) Evaluate the

More information

Algebra 1 Unit 9 Quadratic Equations

Algebra 1 Unit 9 Quadratic Equations Algebra 1 Unit 9 Quadratic Equations Part 1 Name: Period: Date Name of Lesson Notes Tuesda 4/4 Wednesda 4/5 Thursda 4/6 Frida 4/7 Monda 4/10 Tuesda 4/11 Wednesda 4/12 Thursda 4/13 Frida 4/14 Da 1- Quadratic

More information

Name: NOTES 4: APPLICATIONS OF DIFFERENTIATION. Date: Period: Mrs. Nguyen s Initial: WARM UP:

Name: NOTES 4: APPLICATIONS OF DIFFERENTIATION. Date: Period: Mrs. Nguyen s Initial: WARM UP: NOTES 4: APPLICATIONS OF DIFFERENTIATION Name: Date: Period: Mrs. Nguyen s Initial: WARM UP: Assume that f ( ) and g ( ) are differentiable functions: f ( ) f '( ) g ( ) g'( ) - 3 1-5 8-1 -9 7 4 1 0 5

More information

Math 120 Handouts. Functions Worksheet I (will be provided in class) Point Slope Equation of the Line 3. Functions Worksheet III 15

Math 120 Handouts. Functions Worksheet I (will be provided in class) Point Slope Equation of the Line 3. Functions Worksheet III 15 Math 0 Handouts HW # (will be provided to class) Lines: Concepts from Previous Classes (emailed to the class) Parabola Plots # (will be provided in class) Functions Worksheet I (will be provided in class)

More information

Math 120 Handouts. Functions Worksheet I (will be provided in class) Point Slope Equation of the Line 5. Functions Worksheet III 17

Math 120 Handouts. Functions Worksheet I (will be provided in class) Point Slope Equation of the Line 5. Functions Worksheet III 17 Math 0 Handouts HW # (will be provided to class) Lines: Concepts from Previous Classes (emailed to the class) Parabola Plots # (will be provided in class) Functions Worksheet I (will be provided in class)

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

x 20 f ( x ) = x Determine the implied domain of the given function. Express your answer in interval notation.

x 20 f ( x ) = x Determine the implied domain of the given function. Express your answer in interval notation. Test 2 Review 1. Given the following relation: 5 2 + = -6 - y Step 1. Rewrite the relation as a function of. Step 2. Using the answer from step 1, evaluate the function at = -1. Step. Using the answer

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

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

Lesson 5.1 Exercises, pages

Lesson 5.1 Exercises, pages Lesson 5.1 Eercises, pages 346 352 A 4. Use the given graphs to write the solutions of the corresponding quadratic inequalities. a) 2 2-8 - 10 < 0 The solution is the values of for which y

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

Unit 3. Expressions and Equations. 118 Jordan School District

Unit 3. Expressions and Equations. 118 Jordan School District Unit 3 Epressions and Equations 118 Unit 3 Cluster 1 (A.SSE.): Interpret the Structure of Epressions Cluster 1: Interpret the structure of epressions 3.1. Recognize functions that are quadratic in nature

More information

1. The graph of a quadratic function is shown. Each square is one unit.

1. The graph of a quadratic function is shown. Each square is one unit. 1. The graph of a quadratic function is shown. Each square is one unit. a. What is the vertex of the function? b. If the lead coefficient (the value of a) is 1, write the formula for the function in vertex

More information

Math 121. Practice Questions Chapters 2 and 3 Fall Find the other endpoint of the line segment that has the given endpoint and midpoint.

Math 121. Practice Questions Chapters 2 and 3 Fall Find the other endpoint of the line segment that has the given endpoint and midpoint. Math 11. Practice Questions Chapters and 3 Fall 01 1. Find the other endpoint of the line segment that has the given endpoint and midpoint. Endpoint ( 7, ), Midpoint (, ). Solution: Let (, ) denote the

More information

Goal: To graph points in the Cartesian plane, identify functions by graphs and equations, use function notation

Goal: To graph points in the Cartesian plane, identify functions by graphs and equations, use function notation Section -1 Functions Goal: To graph points in the Cartesian plane, identify functions by graphs and equations, use function notation Definition: A rule that produces eactly one output for one input is

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

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

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. Linear equations 1 Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 1) Find the slope of the line passing through the points (, -3) and (2, -1). 1)

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

Baruch College MTH 1030 Sample Final B Form 0809 PAGE 1

Baruch College MTH 1030 Sample Final B Form 0809 PAGE 1 Baruch College MTH 00 Sample Final B Form 0809 PAGE MTH 00 SAMPLE FINAL B BARUCH COLLEGE DEPARTMENT OF MATHEMATICS SPRING 00 PART I (NO PARTIAL CREDIT, NO CALCULATORS ALLOWED). ON THE FINAL EXAM, THERE

More information

7.2 Properties of Graphs

7.2 Properties of Graphs 7. Properties of Graphs of Quadratic Functions GOAL Identif the characteristics of graphs of quadratic functions, and use the graphs to solve problems. LEARN ABOUT the Math Nicolina plas on her school

More information

Ch. 9.3 Vertex to General Form. of a Parabola

Ch. 9.3 Vertex to General Form. of a Parabola Ch. 9.3 Verte to General Form Learning Intentions: of a Parabola Change a quadratic equation from verte to general form. Learn to square a binomial & factor perfectsquare epressions using rectangle diagrams.

More information

?

? NOTES 4: APPLICATIONS OF DIFFERENTIATION Name: Date: Period: WARM UP: Assume that f( ) and g ( ) are differentiable functions: f( ) f '( ) g ( ) g'( ) - 3 1-5 8-1 -9 7 4 1 0 5 9 9-3 1 3-3 6-5 3 8? 1. Let

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 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

Answers. Investigation 2. ACE Assignment Choices. Applications. Problem 2.5. Problem 2.1. Problem 2.2. Problem 2.3. Problem 2.4

Answers. Investigation 2. ACE Assignment Choices. Applications. Problem 2.5. Problem 2.1. Problem 2.2. Problem 2.3. Problem 2.4 Answers Investigation ACE Assignment Choices Problem. Core, Problem. Core, Other Applications ; Connections, 3; unassigned choices from previous problems Problem.3 Core Other Connections, ; unassigned

More information

Section 5.0A Factoring Part 1

Section 5.0A Factoring Part 1 Section 5.0A Factoring Part 1 I. Work Together A. Multiply the following binomials into trinomials. (Write the final result in descending order, i.e., a + b + c ). ( 7)( + 5) ( + 7)( + ) ( + 7)(3 + 5)

More information

CHAPTER 8 Quadratic Equations, Functions, and Inequalities

CHAPTER 8 Quadratic Equations, Functions, and Inequalities CHAPTER Quadratic Equations, Functions, and Inequalities Section. Solving Quadratic Equations: Factoring and Special Forms..................... 7 Section. Completing the Square................... 9 Section.

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

Math 141 Review for Midterm

Math 141 Review for Midterm Math 141 Review for Midterm There will be two parts to this test. Part 1 will have graph sketching, and no calculator is allowed. Part will have everthing else, and a calculator and/or graphing calculator

More information

Review 5 Symbolic Graphical Interplay Name 5.1 Key Features on Graphs Per Date

Review 5 Symbolic Graphical Interplay Name 5.1 Key Features on Graphs Per Date 3 1. Graph the function y = + 3. 4 a. Circle the -intercept. b. Place an on the y-intercept.. Given the linear function with slope ½ and a y-intercept of -: Draw a line on the coordinate grid to graph

More information

MATH 121: EXTRA PRACTICE FOR TEST 2. Disclaimer: Any material covered in class and/or assigned for homework is a fair game for the exam.

MATH 121: EXTRA PRACTICE FOR TEST 2. Disclaimer: Any material covered in class and/or assigned for homework is a fair game for the exam. MATH 121: EXTRA PRACTICE FOR TEST 2 Disclaimer: Any material covered in class and/or assigned for homework is a fair game for the exam. 1 Linear Functions 1. Consider the functions f(x) = 3x + 5 and g(x)

More information

Algebra 2 Unit 2 Practice

Algebra 2 Unit 2 Practice Algebra Unit Practice LESSON 7-1 1. Consider a rectangle that has a perimeter of 80 cm. a. Write a function A(l) that represents the area of the rectangle with length l.. A rectangle has a perimeter of

More information

Practice Problems for Test II

Practice Problems for Test II Math 117 Practice Problems for Test II 1. Let f() = 1/( + 1) 2, and let g() = 1 + 4 3. (a) Calculate (b) Calculate f ( h) f ( ) h g ( z k) g( z) k. Simplify your answer as much as possible. Simplify your

More information

1. A student has learned that test scores in math are determined by this quadratic function:

1. A student has learned that test scores in math are determined by this quadratic function: 01 014 SEMESTER EXAMS 1. A student has learned that test scores in math are determined by this quadratic function: s( t) ( t 6) 99 In the function, s is the score and t is the number of hours that a student

More information

The Quadratic Formula

The Quadratic Formula - The Quadratic Formula Content Standard Reviews A.REI..b Solve quadratic equations by... the quadratic formula... Objectives To solve quadratic equations using the Quadratic Formula To determine the number

More information

Chapter 4. Inequalities

Chapter 4. Inequalities Chapter 4 Inequalities Vannevar Bush, Internet Pioneer 4.1 Inequalities 4. Absolute Value 4.3 Graphing Inequalities with Two Variables Chapter Review Chapter Test 64 Section 4.1 Inequalities Unlike equations,

More information

Quadratic Graphs and Their Properties

Quadratic Graphs and Their Properties - Think About a Plan Quadratic Graphs and Their Properties Physics In a physics class demonstration, a ball is dropped from the roof of a building, feet above the ground. The height h (in feet) of the

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

How can you use multiplication or division to solve an inequality? ACTIVITY: Using a Table to Solve an Inequality

How can you use multiplication or division to solve an inequality? ACTIVITY: Using a Table to Solve an Inequality . Solving Inequalities Using Multiplication or Division How can you use multiplication or division to solve an inequality? 1 ACTIVITY: Using a Table to Solve an Inequality Work with a partner. Copy and

More information

Ready To Go On? Skills Intervention 5-1 Using Transformations to Graph Quadratic Functions

Ready To Go On? Skills Intervention 5-1 Using Transformations to Graph Quadratic Functions Read To Go On? Skills Intervention 5-1 Using Transformations to Graph Quadratic Functions Find these vocabular words in Lesson 5-1 and the Multilingual Glossar. Vocabular quadratic function parabola verte

More information

9.1. Solving Quadratic Equations. Investigation: Rocket Science CONDENSED LESSON

9.1. Solving Quadratic Equations. Investigation: Rocket Science CONDENSED LESSON CONDENSED LESSON 9.1 Solving Quadratic Equations In this lesson you will look at quadratic functions that model projectile motion use tables and graphs to approimate solutions to quadratic equations solve

More information

Math 1101 Chapter 3 Review. 1) f(x) = 2x2 + 2x - 4 A) Concave up B) Concave down. 2) f(x) = -2x2-2x + 2 A) Minimum B) Maximum. 3) f(x) = 0.

Math 1101 Chapter 3 Review. 1) f(x) = 2x2 + 2x - 4 A) Concave up B) Concave down. 2) f(x) = -2x2-2x + 2 A) Minimum B) Maximum. 3) f(x) = 0. Math 11 Chapter 3 Review Determine if the graph of the function is concave up or concave down. 1) f() = + - Concave up B) Concave down Determine if the verte of the graph is a maimum point or a minimum

More information

Writing Quadratic Functions in Standard Form

Writing Quadratic Functions in Standard Form Chapter Summar Ke Terms standard form (general form) of a quadratic function (.1) parabola (.1) leading coefficient (.) second differences (.) vertical motion model (.3) zeros (.3) interval (.3) open interval

More information

UNIT #8 QUADRATIC FUNCTIONS AND THEIR ALGEBRA REVIEW QUESTIONS

UNIT #8 QUADRATIC FUNCTIONS AND THEIR ALGEBRA REVIEW QUESTIONS Answer Ke Name: Date: UNIT #8 QUADRATIC FUNCTIONS AND THEIR ALGEBRA REVIEW QUESTIONS Part I Questions. For the quadratic function shown below, the coordinates of its verte are, (), 7 6,, 6 The verte is

More information

3.4 The Fundamental Theorem of Algebra

3.4 The Fundamental Theorem of Algebra 333371_0304.qxp 12/27/06 1:28 PM Page 291 3.4 The Fundamental Theorem of Algebra Section 3.4 The Fundamental Theorem of Algebra 291 The Fundamental Theorem of Algebra You know that an nth-degree polynomial

More information

TEST REVIEW QUADRATICS EQUATIONS Name: 2. Which of the following statements is true about the graph of the function?

TEST REVIEW QUADRATICS EQUATIONS Name: 2. Which of the following statements is true about the graph of the function? Chapter MATHEMATICS 00 TEST REVIEW QUADRATICS EQUATIONS Name:. Which equation does not represent a quadratic function?. Which of the following statements is true about the graph of the function? it has

More information

REVIEW KEY VOCABULARY REVIEW EXAMPLES AND EXERCISES

REVIEW KEY VOCABULARY REVIEW EXAMPLES AND EXERCISES Etra Eample. Graph.. 6. 7. (, ) (, ) REVIEW KEY VOCABULARY quadratic function, p. 6 standard form of a quadratic function, p. 6 parabola, p. 6 verte, p. 6 ais of smmetr, p. 6 minimum, maimum value, p.

More information

The Quadratic Formula. ax 2 bx c 0 where a 0. Deriving the Quadratic Formula. Isolate the constant on the right side of the equation.

The Quadratic Formula. ax 2 bx c 0 where a 0. Deriving the Quadratic Formula. Isolate the constant on the right side of the equation. SECTION 11.2 11.2 The Quadratic Formula 11.2 OBJECTIVES 1. Solve quadratic equations by using the quadratic formula 2. Determine the nature of the solutions of a quadratic equation by using the discriminant

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

MAT135 Review for Test 4 Dugopolski Sections 7.5, 7.6, 8.1, 8.2, 8.3, 8.4

MAT135 Review for Test 4 Dugopolski Sections 7.5, 7.6, 8.1, 8.2, 8.3, 8.4 Sections 7.5, 7.6, 8.1, 8., 8., 8.4 1. Use the discriminant to determine the number and type(s) of solutions for 4x 8x 4 0. One real solution B. One complex solution Two real solutions Two complex solutions.

More information

4-1 Study Guide and Intervention

4-1 Study Guide and Intervention NAME DATE PERID 4-1 Study Guide and Intervention Graph Quadratic Functions Quadratic Function A function defined by an equation of the form = a 2 + b + c, where a 0 Graph of a Quadratic Function A parabola

More information

Section 5.4 Quadratic Functions

Section 5.4 Quadratic Functions Math 150 c Lynch 1 of 6 Section 5.4 Quadratic Functions Definition. A quadratic function is one that can be written in the form, f(x) = ax 2 + bx + c, where a, b, and c are real numbers and a 0. This if

More information

Unit 10 - Graphing Quadratic Functions

Unit 10 - Graphing Quadratic Functions Unit - Graphing Quadratic Functions PREREQUISITE SKILLS: students should be able to add, subtract and multipl polnomials students should be able to factor polnomials students should be able to identif

More information

Math 150: Intermediate Algebra Spring 2012 Fall 2005 : Mock Exam 4 (z z

Math 150: Intermediate Algebra Spring 2012 Fall 2005 : Mock Exam 4 (z z Math 150: Intermediate Algebra Spring 01 Fall 005 : Mock Eam 4 (z 9. - z NAME 10.6) TICKET # [ 13 problems: 10 points each ] Answer problems and epress your answers appropriately, that is ; simply state

More information

(b) Equation for a parabola: c) Direction of Opening (1) If a is positive, it opens (2) If a is negative, it opens

(b) Equation for a parabola: c) Direction of Opening (1) If a is positive, it opens (2) If a is negative, it opens Section.1 Graphing Quadratics Objectives: 1. Graph Quadratic Functions. Find the ais of symmetry and coordinates of the verte of a parabola.. Model data using a quadratic function. y = 5 I. Think and Discuss

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

Maintaining Mathematical Proficiency

Maintaining Mathematical Proficiency Chapter Maintaining Mathematical Proficienc Find the -intercept of the graph of the linear equation. 1. = + 3. = 3 + 5 3. = 10 75. = ( 9) 5. 7( 10) = +. 5 + 15 = 0 Find the distance between the two points.

More information

MATH 121: EXTRA PRACTICE FOR TEST 2. Disclaimer: Any material covered in class and/or assigned for homework is a fair game for the exam.

MATH 121: EXTRA PRACTICE FOR TEST 2. Disclaimer: Any material covered in class and/or assigned for homework is a fair game for the exam. MATH 121: EXTRA PRACTICE FOR TEST 2 Disclaimer: Any material covered in class and/or assigned for homework is a fair game for the exam. 1 Linear Functions 1. Consider the functions f(x) = 3x + 5 and g(x)

More information

Lesson Goals. Unit 4 Polynomial/Rational Functions Quadratic Functions (Chap 0.3) Family of Quadratic Functions. Parabolas

Lesson Goals. Unit 4 Polynomial/Rational Functions Quadratic Functions (Chap 0.3) Family of Quadratic Functions. Parabolas Unit 4 Polnomial/Rational Functions Quadratic Functions (Chap 0.3) William (Bill) Finch Lesson Goals When ou have completed this lesson ou will: Graph and analze the graphs of quadratic functions. Solve

More information

3.1 Quadratic Functions and Their Models. Quadratic Functions. Graphing a Quadratic Function Using Transformations

3.1 Quadratic Functions and Their Models. Quadratic Functions. Graphing a Quadratic Function Using Transformations 3.1 Quadratic Functions and Their Models Quadratic Functions Graphing a Quadratic Function Using Transformations Graphing a Quadratic Function Using Transformations from Basic Parent Function, ) ( f Equations

More information