1) Explain in complete sentences how to solve the following equation using the factoring method. Y=7x
|
|
- Rodger Preston
- 6 years ago
- Views:
Transcription
1 TEST 13 REVIEW Quadratics 1) Explain in complete sentences how to solve the following equation using the factoring method. Y=7x ) Find the domain and range if the points in the table are discrete Domain: Range: Which best describes the relationship in the table A)1 B) 2 C) x times itself D) Y times itself 3) Find the Axis of Symmetry on the graph below. A) 1 B) -5 C) -1 D) 3
2 Graph this quadratic equation y = 2x 2-16x Solve Quadratic Equation 5x 2 + 9x = Fill in this table y = ½ ( x 4 ) Solve Quadratic Problem You are trying to dunk a basketball. You need to jump 2.5 ft. in the air to dunk the ball. The height that your feet are above the ground in given by the function h(t) = -16t 2 +12t. What s the maximum height your feet will be above the X Y
3 1. Approximate the zeros located on the graph. A. (2,0) (-2,0) B. (0,2) (0,-2) C. (2,0) (0,-2) D. (-3,0) (2,0) 2. What type of graph would the table below represent? X Y A. Quadratic B. Linear C. None of the above 3. I. X 2 II. 3X 2 III. 1/2X 2 IIII. 4X 2 List these equations from narrowest to widest. A. III,I,II,IIII B. IIII,II,I,III C. I,III,II,IIII D. IIII,I,II,III
4
5 1. While on vacation in Italy, Rudy visited the Leaning Tower of Pisa. When he leaned over the railing to look down from the tower, his sunglasses fell off. The height in meters of the sunglasses as they fell can be approximated by the function y= -5x 2 +50, where x is the time in seconds. How long did it take for the glasses to reach the ground 2. Label the vertex, roots, and the axis of symmetry of the parabola. Then find the domain & range. 3. Is this function quadratic? Explain why or why not. 4. If the coefficient of x 2 in the quadratic function below is multiplied by -1/2, how will the graph change? Y=4x 2 5. How does the quadratic function below compare to the quadratic parent function (in terms of the vertex, width, and opening up or down)? Y=4x 2 6. Write an equation that would shift up the vertex of the function Y=4x 2.
6 1. Mathew is working on an equation f(x)=-x 2-4 if he translated by 3 units down which is the most reasonable answer a. Y = -x 2-1 b. Y = 1/3x 2-4 c. Y = -4x 2-4 d. Y = x Graph the following equation: f(x) = 2x 2-6 and approximate the zeros of this equation. a. (2 and 2) b. (3 and 0) c. (2 and 4) d.( 2 and -3 ) 3. Which term best fits the equation 2x 2 -x-15 a. (x-4)(2x+5) b. (x+3)(2x + 5) c.(x-3)(2x + 5) 1. What does the graph of a quadratic equation look like? a. a straight line c. one fixed point b. a parabola d. two curved lines that never meet 2. (ax 2 + bx + c) is: a. the quadratic formula c. not able to be graphed b. a parabola d. the general form of a quadratic equation e. always in all four quadrants when graphed 3. In the quadratic formula the value of x is a. always a vertex c. an intercept b. a solution d. a zero 4. Use the factoring method(gcf) to find the factors for 3x 2 + 6x + 3
7 1. The y-intercept of the equation y=⅓(x+2) 2 +6 is a) Between 5 and 6 b) Between 6 and 7 c) Between 7 and 8 d) Between 8 and 9 2. Which of the following has no real solutions? a) x 2 -x+1=0 b)x 2 -x-1=0 c)x 2 -x-2=0 d)x 2 -x-3=0 3. James kicked a field goal, and wants to figure out how high the ball went in the air. If the path of the football can be represented by -x 2 -x+35, how high did he kick the ball? a) 4 ft b) 10 ft c) 35 ft d) 20 ft 4. Why is this not a quadratic relationship? a) Because the value at zero is one. b) Because X increases at a constant rate. c) Because the ratio of y/x is constant. d) Because the graph of the equations is a parabola. x y KEY: 1C 2A 3C 4C
8 1. Drae, Ethan, and Matthew went to summer camp and rented a canoe. The cost of renting a canoe is modeled by Y = X When Y represents the total cost, X represents the number of hourss rented, and 3 is the one-time cost of entering the store. What is the cost of renting the canoe for three hours? A. $105 C. 3%of entrance fee B. $12 D. $9 2. Write the equation for the graph. What is the solution for Y = 0? 3. Which graph models the equation Y = X ? A. B. Y X B. D. Y X Y X Y X How many solutions are in the equation y = x(x+8)
9 The height of a diver above the water during a dive can be modeled by h=-16t 2 +8t+48, where h is height in feet and t is time in seconds. Find the time it takes for the diver to reach the water. A. t= 3/2x B. t=2/3x C. t= 5/4x D. t= 4/5 What is the line of symmetry in the graph to the right? A. 4 B.7 C.-2 D.2 What is the vertex of the quadratic relationship shown in the table? A. 11 B. -2 C. 4 D. 2 x Y KEY: 1A 2D 3D 2 11
10 1. What is the parent function of the equation y=4x 2-6x+7? a. y=-x b. y=x 2 c. y=x 2 +7 d. y=x+7 2. The area of a new playground is 4x 2 +4x. Find the dimensions (length and width) by factoring. Explain how you got your answer. MUST SHOW ALL WORK! Length: Width: 3. Use the tables below and decide which is a quadratic function. a. c. b.
11 4. (x+2) (x+1) If that is the factoring of a quadratic equation, then which graph matches the factor? a. c. b. Assessment Key 1. B 2. length: 4x width: x+1 3. C 4. A 1.The Area of a rectangle is 4x^2-9. What is the perimeter? A.8x C.4x B.8x+12 D.4x+6 2.A picture has a height that is 4/3 its width. It is to be enlarged to have an area of 192 square inches. What will be the dimensions of the enlargement? A.12 by 15 B.12 by 16 C.-12 by 16 D.13 by 15
12 3.Which equation represents the quadratic that is graphed below? A.y=x(x-2) C.y=-x(x-2) B.y=x(x-2) D.y=-x(x+2) 4.Complete the table for the graph above and find the axis of symmetry Solve. 1) (x+1) (x-3)=0. Answer: X=-1, 3 2) x^2 + x -4 =0. Answer: X= -1+- square root 17 divided by two 3) x^2-3x -4=0. Answer: X=-1, 4 4) x^2-4=0 Answer: X=+-2
13 1. A ball is thrown upward from a height of 15 ft. with an initial upward velocity of 5 ft. / s. Use the formula h(t) = -16t 2 + vt + s to find how long it will take for the ball to hit the ground. 2. Graph the following quadratic equation y = 3x^2 + x + 1 What is the y - intercept? A. (0,-1) B. (-1,0) C. (-.5,0) D. (.5,0) 1. What are the solutions to X 2 +8X =-15 a) a). x=3 and x=5 b) b). x=-15 and x=-3 c) c). x=-3 and x=-5 d) d). x=9 and x=-5 2. Which equation matches the table? a) A). 4x 2 +8x+1 b) B).5x 2 +8x+7 c) C).8x 2 +4x+1 d) D).9x 2 +7x+2 x y
14 3. What are the zeros of this parabola? a) A). -6 and 1 b) B). 8 and -5 c) C). -8 and 1 d) D). 4 and 9 4. The height of a diver above the water during a dive can be modeled by H = -16t 2 + 8t + 48, where H is height in feet and t is time in seconds. Find the time it takes for the diver to reach the water. Write your answer in a complete sentence. Question 1: C Question 2: A Question 3: C Question 4: Its takes the diver 2 seconds.
1) Solve the quadratic equation Y=5x*+3 where *=2 A. x = (Y-3) B. x = (3+Y) C. x = (3+Y) 2 D. x = (Y-3) 2
TEST 13 REVIEW Quadratics 1) Solve the quadratic equation Y=5x*+3 where *=2 A. x = (Y-3) B. x = (3+Y) C. x = (3+Y) 2 D. x = (Y-3) 2 2) Explain in complete sentences how to solve the following equation
More informationQuadratic Functions and Equations
Quadratic Functions and Equations 9A Quadratic Functions 9-1 Quadratic Equations and Functions Lab Explore the Axis of Symmetry 9- Characteristics of Quadratic Functions 9-3 Graphing Quadratic Functions
More informationA. B. C. D. Quadratics Practice Test. Question 1. Select the graph of the quadratic function. g (x ) = 1 3 x 2. 3/8/2018 Print Assignment
Question 1. Select the graph of the quadratic function. g (x ) = 1 3 x 2 C. D. https://my.hrw.com/wwtb2/viewer/printall_vs23.html?umk5tfdnj31tcldd29v4nnzkclztk3w8q6wgvr262aca0a5fsymn1tfv8j1vs4qotwclvofjr8xhs0cldd29v4
More informationSkills Practice Skills Practice for Lesson 3.1
Skills Practice Skills Practice for Lesson. Name Date Lots and Projectiles Introduction to Quadratic Functions Vocabular Define each term in our own words.. quadratic function. vertical motion Problem
More informationAdvAlg6.4GraphingQuadratics.notebook. March 07, Newton s Formula h(t) = 1 gt 2 + v o t + h o 2. time. initial upward velocity
Notes Lesson 6 4 Applications of Quadratic Functions Newton s Formula h(t) = 1 gt 2 + v o t + h o 2 Height of object time Constant (accel. due to gravity) *32 ft/sec 2 *9.8 m/sec 2 **MEMORIZE THESE** initial
More informationFoundations of Math 2 Final A. Which graph would best represent the graph of this parabola if it is translated 4 units down and 6 units left?
Name: Date: 1. The graph of y = x 2 + is shown below. Which graph would best represent the graph of this parabola if it is translated units down and 6 units left? 2. The roots of a quadratic equation can
More informationChapter 5 Smartboard Notes
Name Chapter 5 Smartboard Notes 10.1 Graph ax 2 + c Learning Outcome To graph simple quadratic functions Quadratic function A non linear function that can be written in the standard form y = ax 2 + bx
More information( ) f ( x 1 ) . x 2. To find the average rate of change, use the slope formula, m = f x 2
Common Core Regents Review Functions Quadratic Functions (Graphs) A quadratic function has the form y = ax 2 + bx + c. It is an equation with a degree of two because its highest exponent is 2. The graph
More informationMAT135 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 informationy ax bx c OR 0 then either a = 0 OR b = 0 Steps: 1) if already factored, set each factor in ( ) = 0 and solve
Algebra 1 SOL Review: Quadratics Name 67B Solving Quadratic equations using Zero-Product Property. Quadratic equation: ax bx c 0 OR y ax bx c OR f ( x ) ax bx c Zero-Product Property: if a b 0 then either
More informationMATH 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 informationSolving Quadratic Equations (Adapted from Core Plus Mathematics, Courses 1 and 2)
Solving Quadratic Equations (Adapted from Core Plus Mathematics, Courses 1 and ) In situations that involve quadratic functions, the interesting questions often require solving equations. For example,
More informationAlgebra II Unit #2 4.6 NOTES: Solving Quadratic Equations (More Methods) Block:
Algebra II Unit # Name: 4.6 NOTES: Solving Quadratic Equations (More Methods) Block: (A) Background Skills - Simplifying Radicals To simplify a radical that is not a perfect square: 50 8 300 7 7 98 (B)
More information3 UNIT 4: QUADRATIC FUNCTIONS -- NO CALCULATOR
Name: Algebra Final Exam Review, Part 3 UNIT 4: QUADRATIC FUNCTIONS -- NO CALCULATOR. Solve each of the following equations. Show your steps and find all solutions. a. 3x + 5x = 0 b. x + 5x - 9 = x + c.
More information2. If the discriminant of a quadratic equation is zero, then there (A) are 2 imaginary roots (B) is 1 rational root
Academic Algebra II 1 st Semester Exam Mr. Pleacher Name I. Multiple Choice 1. Which is the solution of x 1 3x + 7? (A) x -4 (B) x 4 (C) x -4 (D) x 4. If the discriminant of a quadratic equation is zero,
More information(a) Write down the value of q and of r. (2) Write down the equation of the axis of symmetry. (1) (c) Find the value of p. (3) (Total 6 marks)
1. Let f(x) = p(x q)(x r). Part of the graph of f is shown below. The graph passes through the points ( 2, 0), (0, 4) and (4, 0). (a) Write down the value of q and of r. (b) Write down the equation of
More informationNO CREDIT DO NOT USE IT
1. Liela is standing on the opponents 40 yard line. She throws a pass toward the goal line. The ball is 2 meters above the ground when she lets go. It follows a parabolic path, reaching its highest point,
More informationALGEBRA UNIT 11-GRAPHING QUADRATICS THE GRAPH OF A QUADRATIC FUNCTION (DAY 1)
ALGEBRA UNIT 11-GRAPHING QUADRATICS THE GRAPH OF A QUADRATIC FUNCTION (DAY 1) The Quadratic Equation is written as: ; this equation has a degree of. Where a, b and c are integer coefficients (where a 0)
More informationRF2 Unit Test # 2 Review Quadratics (Chapter 6) 1. What is the degree of a quadratic function?
RF Unit Test # Review Quadratics (Chapter 6) 1. What is the degree of a quadratic function? Name: a. 1 b. c. 3 d. 0. What is the -intercept for = 3x + x 5? a. 5 b. 5 c. d. 3 3. Which set of data is correct
More informationPAP Algebra 2. Unit 4B. Quadratics (Part 2) Name Period
PAP Algebra Unit 4B Quadratics (Part ) Name Period 1 After Test WS: 4.6 Solve by Factoring PAP Algebra Name Factor. 1. x + 6x + 8. 4x 8x 3 + + 3. x + 7x + 5 4. x 3x 1 + + 5. x + 7x + 6 6. 3x + 10x + 3
More informationStamford Public Schools Mathematics Department. CP Algebra II Mid-Term Exam REVIEW. January 2017
. Stamford Public Schools Mathematics Department CP Algebra II Mid-Term Exam REVIEW January 2017 Student Name: School/Teacher: Date: SPS Math CP Algebra II Midterm Exam Review 2016 2017 CP Algebra 2 Midterm
More informationAlgebra 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 informationThe x-coordinate of the vertex: The equation of the axis of symmetry:
Algebra 2 Notes Section 4.1: Graph Quadratic Functions in Standard Form Objective(s): Vocabulary: I. Quadratic Function: II. Standard Form: III. Parabola: IV. Parent Function for Quadratic Functions: Vertex
More informationChapter 5: Quadratic Functions
Section 5.1: Square Root Property #1-20: Solve the equations using the square root property. 1) x 2 = 16 2) y 2 = 25 3) b 2 = 49 4) a 2 = 16 5) m 2 = 98 6) d 2 = 24 7) x 2 = 75 8) x 2 = 54 9) (x 3) 2 =
More information2 If ax + bx + c = 0, then x = b) What are the x-intercepts of the graph or the real roots of f(x)? Round to 4 decimal places.
Quadratic Formula - Key Background: So far in this course we have solved quadratic equations by the square root method and the factoring method. Each of these methods has its strengths and limitations.
More informationChapter 8 ~ Quadratic Functions and Equations In this chapter you will study... You can use these skills...
Chapter 8 ~ Quadratic Functions and Equations In this chapter you will study... identifying and graphing quadratic functions transforming quadratic equations solving quadratic equations using factoring
More informationNote: The zero function f(x) = 0 is a polynomial function. It has no degree and no leading coefficient. Sep 15 2:51 PM
2.1 Linear and Quadratic Name: Functions and Modeling Objective: Students will be able to recognize and graph linear and quadratic functions, and use these functions to model situations and solve problems.
More informationQuadratic 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 informationUnit 6: Quadratics. Contents
Unit 6: Quadratics Contents Animated gif Program...6-3 Setting Bounds...6-9 Exploring Quadratic Equations...6-17 Finding Zeros by Factoring...6-3 Finding Zeros Using the Quadratic Formula...6-41 Modeling:
More informationCompleting the Square
5-7 Completing the Square TEKS FOCUS TEKS (4)(F) Solve quadratic and square root equations. TEKS (1)(A) Apply mathematics to problems arising in everyday life, society, and the workplace. Additional TEKS
More informationJakarta International School 8 th Grade AG1 Summative Assessment
Jakarta International School 8 th Grade AG1 Summative Assessment Unit 6: Quadratic Functions Name: Date: Grade: Standard Advanced Highly Advanced Unit 6 Learning Goals NP Green Blue Black Radicals and
More informationOverview QUADRATIC FUNCTIONS PATTERNS IN CHANCE
Overview UNIT 7 UNIT 8 QUADRATIC FUNCTIONS Lesson 1 Quadratic Patterns....................... 462 1 Pumpkins in Flight............................... 463 2 Golden Gate Quadratics............................
More informationName Date Class California Standards 17.0, Quadratic Equations and Functions. Step 2: Graph the points. Plot the ordered pairs from your table.
California Standards 17.0, 1.0 9-1 There are three steps to graphing a quadratic function. Graph y x 3. Quadratic Equations and Functions 6 y 6 y x y x 3 5 1 1 0 3 1 1 5 0 x 0 x Step 1: Make a table of
More informationThe coordinates of the vertex of the corresponding parabola are p, q. If a > 0, the parabola opens upward. If a < 0, the parabola opens downward.
Mathematics 10 Page 1 of 8 Quadratic Relations in Vertex Form The expression y ax p q defines a quadratic relation in form. The coordinates of the of the corresponding parabola are p, q. If a > 0, the
More informationName I.D. Number. Select the response that best completes the statement or answers the question.
Name I.D. Number Unit 4 Evaluation Evaluation 04 Second Year Algebra 1 (MTHH 039 059) This evaluation will cover the lessons in this unit. It is open book, meaning you can use your textbook, syllabus,
More information\/ \ i 1. \ I I / 4\ I I1 I. Chapter 7 Review: Quadratics Textbook p Summary: p , p Practice Questions p.398,p.
Chapter 7 Review: Quadratics Textbook p.358-444 Summary: p.396-397, p.441-442 Practice Questions p.398,p.443-444 Key Concepts: Quadratic Analysis, Different Forms of Quadratics, Solving Quadratics, Factoring,
More informationLesson 1: Multiplying and Factoring Polynomial Expressions
Lesson 1 Lesson 1: Multiplying and Factoring Polynomial Expressions When you multiply two terms by two terms you should get four terms. Why is the final result when you multiply two binomials sometimes
More informationPART A CALCULATOR ACTIVE: Maximum Time: 35 Minutes
Algebra II: Chapter 5 Unit Test 2 Name: PART A CALCULATOR ACTIVE: Maximum Time: 35 Minutes Fill in the blanks: Put answers in the space provided. 1. The value of k that makes x 2 + kx + 25 4 a perfect
More informationMATH 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 informationName: Teacher: Per: Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9 Unit 10. Unit 9a. [Quadratic Functions] Unit 9 Quadratics 1
Name: Teacher: Per: Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9 Unit 10 Unit 9a [Quadratic Functions] Unit 9 Quadratics 1 To be a Successful Algebra class, TIGERs will show #TENACITY
More information6.1 Quadratic Expressions, Rectangles, and Squares. 1. What does the word quadratic refer to? 2. What is the general quadratic expression?
Advanced Algebra Chapter 6 - Note Taking Guidelines Complete each Now try problem in your notes and work the problem 6.1 Quadratic Expressions, Rectangles, and Squares 1. What does the word quadratic refer
More informationMs. Peralta s IM3 HW 5.4. HW 5.4 Solving Quadratic Equations. Solve the following exercises. Use factoring and/or the quadratic formula.
HW 5.4 HW 5.4 Solving Quadratic Equations Name: Solve the following exercises. Use factoring and/or the quadratic formula. 1. 2. 3. 4. HW 5.4 5. 6. 4x 2 20x + 25 = 36 7. 8. HW 5.4 9. 10. 11. 75x 2 30x
More informationLesson 7.1 Polynomial Degree and Finite Differences
Lesson 7.1 Polynomial Degree and Finite Differences 1. Identify the degree of each polynomial. a. 3x 4 2x 3 3x 2 x 7 b. x 1 c. 0.2x 1.x 2 3.2x 3 d. 20 16x 2 20x e. x x 2 x 3 x 4 x f. x 2 6x 2x 6 3x 4 8
More informationSubtract 16 from both sides. Divide both sides by 9. b. Will the swing touch the ground? Explain how you know.
REVIEW EXAMPLES 1) Solve 9x + 16 = 0 for x. 9x + 16 = 0 9x = 16 Original equation. Subtract 16 from both sides. 16 x 9 Divide both sides by 9. 16 x Take the square root of both sides. 9 4 x i 3 Evaluate.
More informationGiven the table of values, determine the equation
3.1 Properties of Quadratic Functions Recall: Standard Form f(x) = ax 2 + bx + c Factored Form f(x) = a(x r)(x s) Vertex Form f(x) = a(x h) 2 + k Given the table of values, determine the equation x y 1
More informationCHAPTER 1 QUADRATIC FUNCTIONS AND FACTORING
CHAPTER 1 QUADRATIC FUNCTIONS AND FACTORING Big IDEAS: 1) Graphing and writing quadratic functions in several forms ) Solving quadratic equations using a variety of methods 3) Performing operations with
More information9-4. Quadratics and Projectiles. Vocabulary. Equations for the Paths of Projectiles. Activity. Lesson
Chapter 9 Lesson 9-4 Quadratics and Projectiles Vocabulary force of gravity initial upward velocity initial height BIG IDEA Assuming constant gravity, both the path of a projectile and the height of a
More informationQuadratic Equations. Math 20-1 Chapter 4. General Outcome: Develop algebraic and graphical reasoning through the study of relations.
Math 20-1 Chapter 4 Quadratic Equations General Outcome: Develop algebraic and graphical reasoning through the study of relations. Specific Outcomes: RF1. Factor polynomial expressions of the form: ax
More informationLesson 9 Exploring Graphs of Quadratic Functions
Exploring Graphs of Quadratic Functions Graph the following system of linear inequalities: { y > 1 2 x 5 3x + 2y 14 a What are three points that are solutions to the system of inequalities? b Is the point
More information1 P a g e Province Mathematics Department Southwest Tennessee Community College
Chapter 10 Section 10.1 - Solving Quadratic Equations by the Square Root Property Objectives: 1. Review the zero-factor property. 2. Solve equations of the form x 2 = k, where k > 0. 3. Solve equations
More informationUnit 9: Quadratics Intercept Form
For Teacher Use Packet Score: Name: Period: Algebra 1 Unit 9: Quadratics Intercept Form Note & Homework Packet Date Topic/Assignment HW Page 9-A Graphing Parabolas in Intercept Form 9-B Solve Quadratic
More informationSolving Quadratic Equations: Algebraically and Graphically Read 3.1 / Examples 1 4
CC Algebra II HW #14 Name Period Row Date Solving Quadratic Equations: Algebraically and Graphically Read 3.1 / Examples 1 4 Section 3.1 In Exercises 3 12, solve the equation by graphing. (See Example
More informationUNIT 3: MODELING AND ANALYZING QUADRATIC FUNCTIONS
UNIT 3: MODELING AND ANALYZING QUADRATIC FUNCTIONS This unit investigates quadratic functions. Students study the structure of quadratic expressions and write quadratic expressions in equivalent forms.
More informationAlgebra I EOC Review (Part 2)
1. Let x = total miles the car can travel Answer: x 22 = 18 or x 18 = 22 2. A = 1 2 ah 1 2 bh A = 1 h(a b) 2 2A = h(a b) 2A = h a b Note that when solving for a variable that appears more than once, consider
More informationModeling with quadratic functions Student Activity Sheet 5; use with Exploring Using y = ax 2 + bx + c to model data
1 What relationship is being compared when discussing Pete s shot? Horizontal distance in feet, x Height in feet, y 0 30 60 90 120 150 65 80 90 98 102 100 2 Use a graphing calculator to make a scatterplot
More informationChapter 3 Diagnostic Test
Chapter 3 Diagnostic Test STUDENT BOOK PAGES 130 188 1. Consider the following data. x 4 3 2 1 0 1 2 3 4 y 14 7 2 1 2 1 2 7 14 a) Create a scatter plot, and draw a curve. b) Use your graph to determine
More informationProperties of Graphs of Quadratic Functions
Properties of Graphs of Quadratic Functions y = ax 2 + bx + c 1) For a quadratic function given in standard form a tells us: c is the: 2) Given the equation, state the y-intercept and circle the direction
More informationBemidji Area Schools Outcomes in Mathematics Analysis 1. Based on Minnesota Academic Standards in Mathematics (2007) Page 1 of 5
Understand the concept of function, and identify important features of functions and other relations using symbolic and graphical methods where appropriate. 9..1.1 9..1. 9..1.3 9..1.4 9..1.5 9..1.6 9..1.7
More informationCC Algebra Quadratic Functions Test Review. 1. The graph of the equation y = x 2 is shown below. 4. Which parabola has an axis of symmetry of x = 1?
Name: CC Algebra Quadratic Functions Test Review Date: 1. The graph of the equation y = x 2 is shown below. 4. Which parabola has an axis of symmetry of x = 1? a. c. c. b. d. Which statement best describes
More informationx 2 + x + x 2 x 3 b. x 7 Factor the GCF from each expression Not all may be possible. 1. Find two numbers that sum to 8 and have a product of 12
Factor the GCF from each expression 4 5 1. 15x 3x. 16x 4 Name: a. b. 4 7 3 6 5 3. 18x y 36x y 4x y 5 4. 3x x 3 x 3 c. d. Not all may be possible. 1. Find two numbers that sum to 8 and have a product of
More informationAlgebra I. Slide 1 / 175. Slide 2 / 175. Slide 3 / 175. Quadratics. Table of Contents Key Terms
Slide 1 / 175 Slide 2 / 175 Algebra I Quadratics 2015-11-04 www.njctl.org Key Terms Table of Contents Click on the topic to go to that section Slide 3 / 175 Characteristics of Quadratic Equations Transforming
More informationAlgebra I. Key Terms. Slide 1 / 175 Slide 2 / 175. Slide 3 / 175. Slide 4 / 175. Slide 5 / 175. Slide 6 / 175. Quadratics.
Slide 1 / 175 Slide / 175 Algebra I Quadratics 015-11-04 www.njctl.org Key Terms Slide 3 / 175 Table of Contents Click on the topic to go to that section Slide 4 / 175 Characteristics of Quadratic Equations
More informationExample: f(x) = 2x² + 1 Solution: Math 2 VM Part 5 Quadratic Functions April 25, 2017
Math 2 Variable Manipulation Part 5 Quadratic Functions MATH 1 REVIEW THE CONCEPT OF FUNCTIONS The concept of a function is both a different way of thinking about equations and a different way of notating
More informationAlgebra I Quadratics
1 Algebra I Quadratics 2015-11-04 www.njctl.org 2 Key Terms Table of Contents Click on the topic to go to that section Characteristics of Quadratic Equations Transforming Quadratic Equations Graphing Quadratic
More informationMinnesota State Colleges and Universities Intermediate Algebra Sample Questions
Minnesota State Colleges and Universities Intermediate Algebra Sample Questions 013 The College Board. College Board, ACCUPLACER, WritePlacer and the acorn logo are registered trademarks of the College
More information- a function that can be written in the standard form. - a form of a parabola where and (h, k) is the vertex
4-1 Quadratic Functions and Equations Objectives A2.A.REI.D.6 (formerly A-REI.D.11) Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the
More informationName: Class: Date: Families Multiple Choice Pre-Test. Multiple Choice Identify the choice that best completes the statement or answers the question.
Name: _ Class: _ Date: Families Multiple Choice Pre-Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1 For f( x) = 5x + 1, find f( 4). 19 C 21 1 D 21
More informationtest corrections graphing calculator factoring test
Warm-Up 1. Please turn in your test corrections to the inbox 2. You need your graphing calculator for today s lesson 3. If you need to take your factoring test, please come talk to Ms. Barger before class
More informationUnit 5 Test: 9.1 Quadratic Graphs and Their Properties
Unit 5 Test: 9.1 Quadratic Graphs and Their Properties Quadratic Equation: (Also called PARABOLAS) 1. of the STANDARD form y = ax 2 + bx + c 2. a, b, c are all real numbers and a 0 3. Always have an x
More informationName 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 informationSection 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 informationChapter 2.7 and 7.3. Lecture 5
Chapter 2.7 and 7.3 Chapter 2 Polynomial and Rational Functions 2.1 Complex Numbers 2.2 Quadratic Functions 2.3 Polynomial Functions and Their Graphs 2.4 Dividing Polynomials; Remainder and Factor Theorems
More informationH(t) = 16t Sketch a diagram illustrating the Willis Tower and the path of the baseball as it falls to the ground.
Name Period Date Introduction to Quadratic Functions Activity 2 Imagine yourself standing on the roof of the 1450-foot-high Willis Tower (formerly called the Sears Tower) in Chicago. When you release and
More informationChapter(5( (Quadratic(Equations( 5.1 Factoring when the Leading Coefficient Equals 1
.1 Factoring when the Leading Coefficient Equals 1 1... x 6x 8 x 10x + 9 x + 10x + 1 4. (x )( x + 1). (x + 6)(x 4) 6. x(x 6) 7. (x + )(x + ) 8. not factorable 9. (x 6)(x ) 10. (x + 1)(x ) 11. (x + 7)(x
More informationA2.MidtermRev2015. Algebra 2 Midterm Exam Review Part 1: Multiple Choice (75pts)
Name: UNIT 1 Algebra 2 Midterm Exam Review Part 1: Multiple Choice (75pts) Patterns & Expressions 1. Which of the following is the seventh term in the pattern below? 2. Which of the following is the eighth
More informationQuadratic 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 informationAlgebra 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 informationUNIT 1 UNIT 1: QUADRATIC FUNCTIONS. By the end of this unit, I can. Name:
UNIT 1: QUADRATIC FUNCTIONS UNIT 1 By the end of this unit, I can Draw the graph of a function using different methods Explain the meaning of the term function and distinguish between a function and a
More informationDepartment of Mathematics, University of Wisconsin-Madison Math 114 Worksheet Sections 3.1, 3.3, and 3.5
Department of Mathematics, University of Wisconsin-Madison Math 11 Worksheet Sections 3.1, 3.3, and 3.5 1. For f(x) = 5x + (a) Determine the slope and the y-intercept. f(x) = 5x + is of the form y = mx
More informationPractice Test Questions Multiple Choice Identify the choice that best completes the statement or answers the question.
Practice Test Questions Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which set of data is correct for this graph? 5 y 4 3 1 5 4 3 1 1 1 3 4 5 x 3 4
More informationChapter 4: Quadratic Functions and Factoring 4.1 Graphing Quadratic Functions in Stand
Chapter 4: Quadratic Functions and Factoring 4.1 Graphing Quadratic Functions in Stand VOCAB: a quadratic function in standard form is written y = ax 2 + bx + c, where a 0 A quadratic Function creates
More informationSolutions Key Quadratic Functions
CHAPTER 5 Solutions Key Quadratic Functions ARE YOU READY? PAGE 11 1. E. C. A. B 5. (.) (.)(.) 10. 6. ( 5) ( 5 )( 5 ) 5 7. 11 11 8. 1 16 1 9. 7 6 6 11. 75 75 5 11 15 11 1. (x - )(x - 6) x - 6x - x + 1
More informationLT1: Adding and Subtracting Polynomials. *When subtracting polynomials, distribute the negative to the second parentheses. Then combine like terms.
LT1: Adding and Subtracting Polynomials *When adding polynomials, simply combine like terms. *When subtracting polynomials, distribute the negative to the second parentheses. Then combine like terms. 1.
More informationUNIT 2B QUADRATICS II
UNIT 2B QUADRATICS II M2 12.1-8, M2 12.10, M1 4.4 2B.1 Quadratic Graphs Objective I will be able to identify quadratic functions and their vertices, graph them and adjust the height and width of the parabolas.
More informationPreCalculus Summer Assignment (2018/2019)
PreCalculus Summer Assignment (2018/2019) We are thrilled to have you join the Pre-Calculus family next year, and we want you to get a jump-start over the summer! You have learned so much valuable information
More informationAlgebra 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 informationSY14-15 Algebra Exit Exam - PRACTICE Version
Student Name: Directions: Solve each problem. You have a total of 90 minutes. Choose the best answer and fill in your answer document accordingly. For questions requiring a written response, write your
More informationQuadratic Functions. and Equations
Name: Quadratic Functions and Equations 1. + x 2 is a parabola 2. - x 2 is a parabola 3. A quadratic function is in the form ax 2 + bx + c, where a and is the y-intercept 4. Equation of the Axis of Symmetry
More informationSolving Multi-Step Equations
1. Clear parentheses using the distributive property. 2. Combine like terms within each side of the equal sign. Solving Multi-Step Equations 3. Add/subtract terms to both sides of the equation to get the
More informationTuesday, 3/28 : Ch. 9.8 Cubic Functions ~ Ch. 9 Packet p.67 #(1-6) Thursday, 3/30 : Ch. 9.8 Rational Expressions ~ Ch. 9 Packet p.
Ch. 9.8 Cubic Functions & Ch. 9.8 Rational Expressions Learning Intentions: Explore general patterns & characteristics of cubic functions. Learn formulas that model the areas of squares & the volumes of
More information5-5 Solving Polynomial Equations
Factor completely. If the polynomial is not factorable, write prime. 1. 3ax + 2ay az + 3bx + 2by bz (a + b)(3x + 2y z) 2. 2kx + 4mx 2nx 3ky 6my + 3ny (2x 3y)(k + 2m n) 3. 2x 3 + 5y 3 prime 4. 16g 3 + 2h
More informationIntermediate Algebra Final Exam Review
Intermediate Algebra Final Exam Review Note to students: The final exam for MAT10, MAT 11 and MAT1 will consist of 30 multiple-choice questions and a few open-ended questions. The exam itself will cover
More informationAlgebra 2 Honors. Unit 4, Day 1 Period: Date: Graph Quadratic Functions in Standard Form. (Three more problems on the back )
Algebra Honors Name: Unit 4, Day 1 Period: Date: Graph Quadratic Functions in Standard Form 1. y = 3x. y = 5x + 1 3. y = x 5 4. y = 1 5 x 6. y = x + x + 1 7. f(x) = 6x 4x 5 (Three more problems on the
More informationReading Mathematical Expressions & Arithmetic Operations Expression Reads Note
Math 001 - Term 171 Reading Mathematical Expressions & Arithmetic Operations Expression Reads Note x A x belongs to A,x is in A Between an element and a set. A B A is a subset of B Between two sets. φ
More informationThere are two types of solutions
There are two types of solutions 1) Real solutions which are also x intercept(s) on the graph of the parabola b 2 4ac > 0 b 2 4ac = 0 2) Non real solutions which are not x intercept(s) on the graph of
More informationAlgebra B Chapter 9 Unit Test Version 1 of 3
Name Per. _ Date Algebra B Chapter 9 Unit Test Version 1 of 3 Instructions: 1. Reduce all radicals to simplest terms. Do not approximate square roots as decimals. 2. Place your name, period and the date
More informationName. 1. Given the solution (3, y), what is the value of y if x + y = 6? 7. The graph of y = x 2 is shown below. A. 3 B. 4 C. 5 D.
Name 1. Given the solution (, y), what is the value of y if x + y = 6? 7. The graph of y = x is shown below. 5 D. 6. What are the solutions to the equation x - x = 0? x = - or x = - x = - or x = 1 x =
More informationAlgebra 1. Math Review Packet. Equations, Inequalities, Linear Functions, Linear Systems, Exponents, Polynomials, Factoring, Quadratics, Radicals
Algebra 1 Math Review Packet Equations, Inequalities, Linear Functions, Linear Systems, Exponents, Polynomials, Factoring, Quadratics, Radicals 2017 Math in the Middle 1. Clear parentheses using the distributive
More information3.4 Solving Quadratic Equations by Completing
.4. Solving Quadratic Equations by Completing the Square www.ck1.org.4 Solving Quadratic Equations by Completing the Square Learning objectives Complete the square of a quadratic expression. Solve quadratic
More informationCP Algebra 2 Midterm Review Multiple Choice (40 questions)
CP Algebra 2 Midterm Review Multiple Choice (40 questions) Evaluate each expression if r = -1, n = 3, t = 12, and w = 1 2. 1. w[t + (t r)] 2. 9r 2 + (n 2 1)t Solve each equation. Check your solution. 3.
More information