Skills Practice Skills Practice for Lesson 1.1

Similar documents
Skills Practice Skills Practice for Lesson 3.1

Writing Quadratic Functions in Standard Form

REVIEW KEY VOCABULARY REVIEW EXAMPLES AND EXERCISES

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

Algebra 1 Unit 9 Quadratic Equations

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

Solve Quadratic Equations by Graphing

Maintaining Mathematical Proficiency

Quadratic Functions Objective: To be able to graph a quadratic function and identify the vertex and the roots.

20.2 Connecting Intercepts and Linear Factors

Vertex form of a quadratic equation

6.1 Solving Quadratic Equations by Graphing Algebra 2

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

Unit 10 - Graphing Quadratic Functions

Path of the Horse s Jump y 3. transformation of the graph of the parent quadratic function, y 5 x 2.

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

Attributes and Transformations of Quadratic Functions VOCABULARY. Maximum value the greatest. Minimum value the least. Parabola the set of points in a

7.2 Connecting Intercepts and Linear Factors

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

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

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

Maintaining Mathematical Proficiency

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

9-1. The Function with Equation y = ax 2. Vocabulary. Graphing y = x 2. Lesson

The Coordinate Plane. Circles and Polygons on the Coordinate Plane. LESSON 13.1 Skills Practice. Problem Set

Mini-Lecture 8.1 Solving Quadratic Equations by Completing the Square

Section 2.5: Graphs of Functions

C H A P T E R 3 Polynomial Functions

3.1 Graph Quadratic Functions

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

1. Without the use of your calculator, evaluate each of the following quadratic functions for the specified input values. (c) ( )

Using Intercept Form

NAME DATE PERIOD. Study Guide and Intervention. Transformations of Quadratic Graphs

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

4.2 Parabolas. Explore Deriving the Standard-Form Equation. Houghton Mifflin Harcourt Publishing Company. (x - p) 2 + y 2 = (x + p) 2

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

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

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

Algebra I Quadratics Practice Questions

UNIT #8 QUADRATIC FUNCTIONS AND THEIR ALGEBRA REVIEW QUESTIONS

Graph Quadratic Functions in Standard Form

Graphs and Solutions for Quadratic Equations

For questions 5-8, solve each inequality and graph the solution set. You must show work for full credit. (2 pts each)

3 Polynomial and Rational Functions

2 nd Semester Final Exam Review Block Date

Essential Question How can you use a quadratic function to model a real-life situation?

f(x) = 2x 2 + 2x - 4

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

Algebra II Practice Test Quadratic Functions Unit 3 Part II. Period Date NON-CALCULATOR SECTION

Final Exam Review Part 2 #1 Page 1 / 21

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

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

Lesson 7.1 Polynomial Degree and Finite Differences

x Radical Sign: Radicand: the number beneath the radical sign

Chapter 2 Polynomial, Power, and Rational Functions

Mt. Douglas Secondary

d. 2x 3 7x 2 5x 2 2x 2 3x 1 x 2x 3 3x 2 1x 2 4x 2 6x 2 3. a. x 5 x x 2 5x 5 5x 25 b. x 4 2x 2x 2 8x 3 3x 12 c. x 6 x x 2 6x 6 6x 36

Section 2.3 Quadratic Functions and Models

MATH 115: Review for Chapter 3

6.3 Interpreting Vertex Form and Standard Form

Chapter 9 Notes Alg. 1H 9-A1 (Lesson 9-3) Solving Quadratic Equations by Finding the Square Root and Completing the Square

2 nd Semester Final Exam Review Block Date

3.1-Quadratic Functions & Inequalities

Characteristics of Quadratic Functions

ALGEBRA II-GRAPHING QUADRATICS THE GRAPH OF A QUADRATIC FUNCTION

Name Class Date. Solving by Graphing and Algebraically

Practice Problems for Test II

10.4 Nonlinear Inequalities and Systems of Inequalities. OBJECTIVES 1 Graph a Nonlinear Inequality. 2 Graph a System of Nonlinear Inequalities.

The slope, m, compares the change in y-values to the change in x-values. Use the points (2, 4) and (6, 6) to determine the slope.

5-4. Focus and Directrix of a Parabola. Key Concept Parabola VOCABULARY TEKS FOCUS ESSENTIAL UNDERSTANDING

Ready To Go On? Skills Intervention 10-1 Introduction to Conic Sections

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

1.5. Analyzing Graphs of Functions. The Graph of a Function. What you should learn. Why you should learn it. 54 Chapter 1 Functions and Their Graphs

Name Date Class California Standards 17.0, Quadratic Equations and Functions. Step 2: Graph the points. Plot the ordered pairs from your table.

QUEEN ELIZABETH REGIONAL HIGH SCHOOL MATHEMATICS 2201 MIDTERM EXAM JANUARY 2015 PART A: MULTIPLE CHOICE ANSWER SHEET

Write Quadratic Functions and Models

C H A P T E R 9 Topics in Analytic Geometry

College Algebra ~ Review for Test 2 Sections

Final Exam Review Part 2 #4

Final Exam Review Part 2 #4

Lesson 9.1 Using the Distance Formula

SECTION 3.1: Quadratic Functions

Comparing Linear and Nonlinear Functions 5.5. ACTIVITY: Finding Patterns for Similar Figures. How can you recognize when a pattern

Polynomial and Rational Functions

2 variables. is the same value as the solution of. 1 variable. You can use similar reasoning to solve quadratic equations. Work with a partner.

1-D and 2-D Motion Test Friday 9/8

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?

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

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

Review Exercises for Chapter 2

CHAPTER 2 Polynomial and Rational Functions

MATH 111 Departmental Midterm Exam Review Exam date: Tuesday, March 1 st. Exam will cover sections and will be NON-CALCULATOR EXAM.

Name Class Date. Deriving the Standard-Form Equation of a Parabola

Study Guide and Intervention

Algebra 2 Unit 2 Practice

UNIT 2 QUADRATIC FUNCTIONS AND MODELING Lesson 2: Interpreting Quadratic Functions Instruction

( ) f ( x 1 ) . x 2. To find the average rate of change, use the slope formula, m = f x 2

MCF3MI Unit 3: Solving Quadratic Equations

TRANSFORMATIONS OF f(x) = x Example 1

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

Transcription:

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 6 t 0t, where s is the height after t seconds. The acceleration from gravit is 3 feet per second squared, the initial velocit is 0 feet per second, and the initial height is feet. Problem Set Write an equation to represent the area of each rectangle.. A rectangle with a length that is 3 inches longer than its width A w(w 3) w 3w. A rectangle with a length that is inches shorter than its width A w(w ) w w 3. A rectangle with a width that is 8 feet shorter than its length A ( 8) 8. A rectangle with a width that is.6 feet longer than its length A (.6).6 Chapter l Skills Practice 5

Use the given information to answer the questions. 5. A neighborhood is made up of a series of square lots. Due to an increase in bike traffic, a bike lane is being added along the edge of the roadwa. The bike lane will decrease one side of each lot b feet. The equation A w(w ) represents the new area of each lot, where w is the width of the original lot. a. What is the new area of a lot that had an original width of 00 feet? A 00(00 ) 00(88) 37,600 square feet b. What is the new area of a lot that had an original width of 30 feet? A 30(30 ) 30(308) 98,560 square feet 6. A series of picture frames are made so that each has a length that is inches greater than its width. The equation A w w represents the area of each frame, where w is the width of the frame. a. What is the area of a frame with a width of 8 inches? A 8 (8) 6 6 80 square inches b. What is the area of a frame with a width of inches? A () 68 square inches Complete each table. 7. 8. 7 3 7 0 0 0 0 9 0 6 3 39 3 8 60 76 5 Chapter l Skills Practice

Name Date 9. 0. 0 6 0 6 7 66 8 0 500 5 70 3 806 0 0 Create a scatter plot of each data set.. 50 0 0 3 8 3 5 5 35 6 8 5 0 35 30 5 0 5 0 5 0 3 5 6 7 8 9 0. 0 0 6 3 5 8 5 5 50 5 0 35 30 5 0 5 0 5 0 3 5 6 7 8 9 0 Chapter l Skills Practice 53

3. 3 0 0 8 3 0 5 65 80 7 6 56 8 0 3 6 8 0 3 5 6 7 8 9 0. 3 0 0 5 3 7 5 65 6 90 00 90 80 70 60 50 0 30 0 0 0 3 5 6 7 8 9 0 5 Chapter l Skills Practice

Name Date Use the given information to answer the questions. 5. A soccer ball is kicked upward with an initial velocit of 8 feet per second. The acceleration due to gravit is 3 feet per second squared. The equation s 6 t 8t represents the height of the ball, s, after t seconds. What is the height of the ball after a. second? s 6 () 8() s 6 8 s 3 The ball will be 3 feet in the air after second. b. 3 seconds? s 6 (3) 8(3) s 6(9) s s 0 The ball will be 0 feet in the air, or on the ground, after 3 seconds. 6. An arrow is shot upward with an initial velocit of 0 meters per second. The acceleration due to gravit is approimatel 0 meters per second squared. The equation s 0t 5 t represents the height of the arrow, s, after t seconds. What is the height of the arrow after a. seconds? s 0() 5 () s 80 5() s 80 0 s 60 The arrow will be 60 feet in the air after seconds. b. 5 seconds? s 0(5) 5 (5) s 00 5(5) s 00 5 s 75 The arrow will be 75 feet in the air after 5 seconds. Chapter l Skills Practice 55

56 Chapter l Skills Practice

Skills Practice Skills Practice for Lesson. Name Date Parabolas Properties of the Graphs of Quadratic Functions Vocabular Identif and label each term in the diagram. ais of smmetr 0. parabola. verte 3. ais of smmetr. zeros parabola 0 8 6 zeros 6 8 0 verte 0 Problem Set Complete the table for each quadratic function... 8 3 8 3 8 0 0 0 0 0 3 3 8 8 3 8 Chapter l Skills Practice 57

3. 5. 3 3 0 3 6 0 5 0 5 3 6 3 6 Use each table to construct a graph of the given function. 5. 3 7 0 3 7 9 8 7 6 5 3 5 3 0 3 5 6. 6 0 0 0 6 5 3 7 6 5 3 0 3 5 3 58 Chapter l Skills Practice

Name 7. Date 7 0 7 5 3 0 3 5 3 5 7 8. 3 7 0 3 7 5 3 0 3 5 7 3 5 Use the given graph to determine the verte, ais of smmetr, and zeros of the parabola. 9. Ais of smmetr: Zeros: (0, 0) and (, 0) Verte: (, 3) 6 5 3 3 0 3 5 6 3 Chapter l Skills Practice 59

0. Ais of smmetr: Zeros: (, 0) and (0, 0) Verte: (, 3) 5 3 5 3 0 3 5 3 5. Ais of smmetr: Zeros: (, 0) and (0, 0) Verte: (, ) 5 3 0 3 5 3 5 7. Ais of smmetr: 0 Zeros: (, 0) and (, 0) Verte: (0, ) 5 3 3 0 3 5 3 5 7 60 Chapter l Skills Practice

Name Date Use the information provided to determine the ais of smmetr, -intercept(s), and -intercept of the parabola. 3. The verte of the parabola is (, 3) and it passes through the point (0, 0). Ais of smmetr: -intercept(s): (0, 0) and (, 0) -intercept: (0, 0). The verte of the parabola is (, 0) and it passes through the point (0, 6). Ais of smmetr: -intercept(s): (, 0) -intercept: (0, 6) 5. The verte of the parabola is (3, 0) and it passes through the point (0, 8). Ais of smmetr: 3 -intercept(s): (3, 0) -intercept: (0, 8) 6. The verte of the parabola is (, ) and it passes through the point (0, 0). Ais of smmetr: -intercept(s): (0, 0) and (8, 0) -intercept: (0, 0) Chapter l Skills Practice 6

6 Chapter l Skills Practice

Skills Practice Skills Practice for Lesson.3 Name Date Etremes Increase, Decrease, and Rates of Change Vocabular Write the term that best completes each statement.. The rate of change of the unit rate of change is called the second difference.. A minimum or maimum point on a graph, such as the verte of a parabola, is called a(n) etreme point. 3. A(n) interval is the set of numbers between two given numbers.. A(n) open interval (a, b) is the set of all numbers between a and b, but not including a or b. 5. A(n) closed interval [a, b] is the set of all numbers between a and b, including a and b. 6. The notation [a, b) is used for the half-closed interval that is the set of all numbers between a and b that includes a, but does not include b. Problem Set Complete the table for each of the given quadratic functions.. 5. 0 5 3 3 5 0 3 3 7 7 3 3 6 Chapter l Skills Practice 63

3. 3. 3 3 0 3 6 5 0 0 3 0 5 0 3 3 Complete the table for each function b finding the change in and and the unit rate of change (slope) between each pair of points. 5. 6. m 8 3 3 5 5 0 3 3 0 0 3 3 3 8 5 5 m 3 8 8 0 0 6 6 0 0 8 6 6 3 8 0 0 6 Chapter l Skills Practice

Name Date 7. m 5 3 3 0 5 3 3 8. m 7 6 3 0 7 6 3 Complete the table for each function b finding the unit rate of change ( ) and the second difference ( ). 9. ( ) 9 3 5 3 5 0 6 7 3 Chapter l Skills Practice 65

0. ( ) 5 0 5 0 3 3 3 3 0 3. ( ) 3 6 0 0 0 0 6. ( ) 3 0 6 0 6 0 0 66 Chapter l Skills Practice

Name Date Use interval notation to represent each set of numbers. 3. The set of all real numbers between 6 and 6, including 6 and 6 [ 6, 6]. The set of all real numbers between and 0, not including or 0 (, 0) 5. The set of all real numbers between 9 and 0, including 9 but not including 0 [ 9, 0) 6. The set of all real numbers between 5 and, including but not including 5 ( 5, ] 7. The set of all real numbers greater than (, ) 8. The set of all real numbers less than or equal to 6 (, 6] Determine the intervals over which each quadratic function is increasing or decreasing. 9. 0. 6 5 3 0 3 5 3 5 3 5 3 0 3 5 6 7 7 3 The function is increasing over the interval (, ) and decreasing over the interval (, ) The function is decreasing over the interval (, 3) and increasing over the interval (3, ) Chapter l Skills Practice 67

. 6. 8 5 7 6 3 5 3 0 3 5 6 7 3 3 5 3 0 3 The function is decreasing over the interval (, ) and increasing over the interval (, + ). The function is increasing over the interval (, ) and decreasing over the interval (, + ). 68 Chapter l Skills Practice

Skills Practice Skills Practice for Lesson. Name Date Solving Quadratic Equations Reviewing Roots and Zeros Vocabular Describe how to find the roots of a quadratic equation b using the given method.. factoring If a quadratic equation is factorable, first set the equation equal to zero. Then factor the equation and set each factor equal to zero. Solve each resulting equation. The solutions to the resulting equations are the roots, or zeros, of the quadratic equation.. etracting the square roots If a quadratic equation does not have an -term (or if the -terms cancel out), solve the equation for a perfect square. Then, etract the square roots to determine the roots, or zeros, of the quadratic equation. Problem Set Calculate the roots of each quadratic equation b factoring. Check our answers.. 7 0 0 7 0 0 ( 5)( ) 0 5 0 or 0 5 or ( 5 ) 7( 5) 0 5 35 0 0 ( ) 7( ) 0 0 0 Chapter l Skills Practice 69

. 3 0 3 0 ( 3)( ) 0 3 0 or 0 3 or (3 ) (3) 3 9 6 3 0 ( ) ( ) 3 3 0 3. 3 8 3 8 0 ( 7)( ) 0 7 0 or 0 7 or (7) 3(7) 9 8 ( ) 3( ) 6 8. 33 8 8 33 0 ( )( 3) 0 0 or 3 0 or 3 ( ) ; 33 8( ) 33 88 (3 ) 9; 33 8(3) 33 9 70 Chapter l Skills Practice

Name Date 5. 7 7 0 ( )( ) 0 0 or 0 or ( ) 7 ( ) 7 ( ) 7( ) 6 68 6 6. 3 3 0 (3 )( ) 0 3 0 or 0 3 or 3 3 ; 3 ( 3 ) 3 ( 9 ) 3 3; 3( ) 3 7. 5 5 0 ( 5)( 5) 0 5 0 or 5 0 5 or 5 ( 5 ) ( 5 ( 5 ) ( 5 ) 5 ) 5 Chapter l Skills Practice 7

8. 6 3 6 6 3 6 0 (3 )( 3) 0 3 0 or 3 0 3 or 3 6 3 ( 3 ) 6 6 3 8 3 ; 6 ( 6 3 ( 3 ) 6 39 3 ) 6 ( 7 ; 6 ( 3 ) 6 ( 9 9 ) 8 3 ) 7 Find the roots of each quadratic equation b etracting the square roots. Check our answers. 9. 5 5 5 5 5 5 5 5(5 ) 5(5) 5 5( 5 ) 5(5) 5 0. 3 3 0 3 3 8 8 9 3(9 ) 3 3(8) 3 0 3( 9 ) 3 3(8) 3 0 7 Chapter l Skills Practice

Name Date. ( ) 9 9 9 9 7 7(7 ) 7(9) 63 9 (7) 9 63; 7( 7 ) 7( 5) 35 9 ( 7) 9 35. ( ) 9 9 9 0 9 9 3 3(3 ) 9 3( ) 9 (3) ; 3( 3 ) 9 3( 7) 9 ( 3) 3. 5 5 5 5 0 5 5 5 5 5 ( 5 ) ( 5 ) 5 5 5 5 5 5 5 5( 5 ) ( 5 ) 5 5 5 5 5 5 Chapter l Skills Practice 73

. 0 7 7 7 ( 7 ) ( 7 ) 7 7 ( 7 ) ( 7 ) 7 7 5. 3 ( ) 6( ) 3 6 3 6 6 3 3 6 3 3 3 ( ) 3 () 3() 6( ) 6() ; 3 ( ) 3 (0) 0 6( ) 6(0) 0 6. ( ) 0 0 0 8 ( ) () () 0 () 0 8 ; ( ) ( 3) (9) 8 0 ( ) 0 8 8 7 Chapter l Skills Practice

Skills Practice Skills Practice for Lesson.5 Name Date Finding the Middle Determining the Verte of a Quadratic Function Vocabular Describe how to determine the coordinates of the verte for each parabola.. a c, where a and c are real numbers and a is not equal to zero For all quadratic functions in this form, the ais of smmetr is on the -ais ( 0), so the -value of the verte is 0. The -value is c. The coordinates of the verte are (0, c).. a b c, where a, b, and c are real numbers and a and b are not equal to zero To find the verte of a quadratic equation in the form a b c, with b 0, first find the -intercept b evaluating the function at 0. Find the coordinates of the point smmetric to the -intercept b substituting the -coordinate of the -intercept into the equation. Use the midpoint formula on the two points to find the equation for the ais of smmetr. The -coordinate of the verte lies on the ais of smmetr. Calculate the -coordinate b evaluating the function at this -coordinate. Problem Set Determine the ais of smmetr and the verte for each quadratic function.. 6 3 Ais of smmetr: 0 Verte: (0, 3). 9 9 Ais of smmetr: 0 Verte: (0, 9) 3. 7 Ais of smmetr: 0 Verte: (0, 7). 5 8 Ais of smmetr: 0 Verte: (0, 8) 5. ( ) Ais of smmetr: 0 Verte: (0, ) 6. ( ) Ais of smmetr: 0 Verte: (0, ) 7. Ais of smmetr: 0 Verte: (0, ) 8. 3 Ais of smmetr: 0 Verte: (0, ) 9. 6( 3) Ais of smmetr: 0 Verte: (0, 8) 0. ( ) Ais of smmetr: 0 Verte: (0, ) Chapter l Skills Practice 75

Determine whether the verte for each quadratic function is a maimum or minimum.. 3 minimum. 8 3 maimum 3. 7 maimum. minimum 5. ( 7 6) minimum 6. 5( ) maimum 7. (3 ) maimum 8. 3( ) minimum Determine the -intercept of the graph of each quadratic function. 9. 3 (0 ) 3(0) 0 0 -intercept: (0, ) 0. 6 3 3 6(0 ) 3(0) 3 0 0 3 3 -intercept: (0, 3). 6 (0) (0) 6 0 0 6 6 -intercept: (0, 6). 3 3 (0 ) 3(0) 3 0 0 3 3 -intercept: (0, 3) 76 Chapter l Skills Practice

Name Date 3. 3 8 3(0 ) (0) 8 0 0 8 8 -intercept: (0, 8). ( ) ((0 ) (0) ) () -intercept: (0, ) Calculate the ais of smmetr for each set of smmetric points on a parabola. 5. (, 3) and (6, 3) 6 (, 3 3 ) (9, 3) Ais of smmetr: 9 6. (, ) and (6, ) ( 6, ( ) ) (5, ) Ais of smmetr: 5 7. ( 3, 8) and ( 9, 8) ( 3 ( 9) 8, ( 8) ) ( 6, 8) Ais of smmetr: 6 8. (, 5) and (, 5) (, 5 5 ) ( 5, 5) Ais of smmetr: 5 Chapter l Skills Practice 77

Find the coordinates of the point that is smmetric to the given -intercept for each quadratic function. 9. ( ), -intercept: (0, ) ( ) 0 0 ( ) 0 or 0 0 or ( 0 0 ) () ( ( ) ) () Point smmetric to -intercept: (, ) 30. 8 85, -intercept: (0, 85) 85 8 85 0 8 0 ( 8) 0 or 8 0 0 or 8 (0) 8(0) 85 0 0 85 85 ( 8) 8( 8) 85 3 3 85 85 Point smmetric to -intercept: ( 8, 85) 78 Chapter l Skills Practice

Name Date 3. 3, -intercept: (0, 3) 3 3 0 0 ( ) 0 or 0 0 or (0 ) (0) 3 0 0 3 3 ( ) () 3 6 6 3 3 Point smmetric to -intercept: (, 3) 3. (3 ), -intercept: (0, 8) 8 (3 ) 3 0 (3 ) 0 or 3 0 0 or 3 0 or 3 (3(0 ) (0) ) (0 0 ) ( ) 8 ( 3 ( 3 ) ( 3 ) ) ( 3 ( 9 ) ( 3 ) ) ( 3 Point smmetric to -intercept: ( 3, 8 ) 3 ) ( ) 8 Chapter l Skills Practice 79

Use the -intercept and a smmetric point to find the coordinates for the verte of each quadratic function. 33. 0 -intercept: (0, 0) 0 0 0 0 ( ) 0 or 0 0 or 0 (0) 0 0 0 0 0 ( ) () 0 0 0 Smmetric point: (, 0) -coordinate of verte: 0 6 -coordinate of verte: (6) (6) 0 36 7 0 6 Verte: (6, 6) 3. 0 5 -intercept: (0, 5) 5 0 5 0 0 0 ( 0) 0 or 0 0 0 or 0 (0 ) 0(0) 5 0 0 5 5 ( 0 ) 0( 0) 5 00 00 5 5 Smmetric point: ( 0, 5) 0 ( 0) -coordinate of verte: 5 -coordinate of verte: ( 5) 0( 5) 5 5 50 5 0 Verte: ( 5, 0) 80 Chapter l Skills Practice

Name Date 35. 5 -intercept: (0, 5) 5 5 0 0 ( ) 0 or 0 0 or (0) (0) 5 0 0 5 5 ( ) ( ) 5 5 5 Smmetric point: (, 5) 0 ( ) -coordinate of verte: -coordinate of verte: ( ) ( ) 5 5 6 Verte: (, 6) 36. 0 3 -intercept: (0, 3) 3 0 3 0 0 0 ( 0) 0 or 0 0 0 or 0 (0) 0(0) 3 0 0 3 3 (0) 0(0) 3 00 00 3 3 Smmetric point: (0, 3) -coordinate of verte: 0 0 5 -coordinate of verte: (5) 0(5) 3 5 50 3 Verte: (5, ) Chapter l Skills Practice 8

8 Chapter l Skills Practice

Skills Practice Skills Practice for Lesson.6 Name Date Other Forms of Quadratic Functions Verte Form of a Quadratic Function Vocabular Answer each question about the given function.. What form is the quadratic function a b c written in? What do the variables a, b, and c tell ou about the graph of the function? The quadratic function a b c is in standard form. The variable a tells what direction the parabola opens. For a 0, the parabola opens up. For a 0, the parabola opens down. If the variable b 0, the verte of the parabola is on the -ais. The variable c is the -coordinate of the -intercept.. What form is the quadratic function a ( h) k written in? What do the variables a, h, and k tell ou about the graph of the function? The quadratic function a ( h) k is written in verte form. The variable a tells what direction the parabola opens. For a 0, the parabola opens up. For a 0, the parabola opens down. The variable h is the -coordinate of the verte. The variable k is the -coordinate of the verte. Problem Set Use the standard form of each quadratic function to determine the ais of smmetr, the coordinates of the verte, and whether the parabola opens up or down.. f( ) Ais of smmetr: b a ( ) f( ) () () 8 Verte: (, ) a 0, so the parabola opens up. Chapter l Skills Practice 83

. f( ) 8 Ais of smmetr: b a 8 f( ) ( ) 8( ) 6 3 0 Verte: (, 0) a 0, so the parabola opens up. 3. f( ) 6 Ais of smmetr: b a ( ) 6 f( ) (6) (6) 6 (36) 6 7 6 56 Verte: (6, 56) a 0, so the parabola opens up.. f( ) 3 8 Ais of smmetr: b a ( 8 6 ) ( 3) 3 f( ) 3 (3) 8(3) 3(9) 5 7 5 6 Verte: (3, 6) a 0, so the parabola opens down. 5. f( ) Ais of smmetr: 0 Verte: (0, ) a 0, so the parabola opens down. 6. f( ) 9 Ais of smmetr: 0 Verte: (0, 9) a 0, so the parabola opens up. 8 Chapter l Skills Practice

Name Date Use the verte form of each quadratic function to find the ais of smmetr, the coordinates of the verte, and whether the parabola opens up or down. 7. f( ) ( ) Ais of smmetr: Verte: (, ) a 0, so the parabola opens up. 8. f( ) 3 ( ) Ais of smmetr: Verte: (, ) a 0, so the parabola opens up. 9. f( ) 6 ( ) Ais of smmetr: Verte: (, ) a 0, so the parabola opens down. 0. f( ) ( 3) 7 Ais of smmetr: 3 Verte: (3, 7) a 0, so the parabola opens down.. f( ) ( 3) Ais of smmetr: 3 Verte: (3, ) a 0, so the parabola opens up.. f( ) ( ) 3 Ais of smmetr: Verte: (, 3) a 0, so the parabola opens down. Chapter l Skills Practice 85

3. f( ) 8 ( ) 3 Ais of smmetr: Verte: (, 3) a 0, so the parabola opens down.. f( ) 5 ( ) Ais of smmetr: Verte: (, ) a 0, so the parabola opens up. Convert each quadratic function from verte form to standard form. 5. f( ) 6 ( ) f( ) 6( ) f( ) 6 f( ) 6 3 6. f( ) ( 3) 7 f( ) ( 6 9) 7 f( ) 36 7 f( ) 9 7. f( ) ( 3) f( ) ( 6 9) f( ) 6 8 8. f( ) ( ) 3 f( ) ( ) 3 f( ) 3 f( ) 86 Chapter l Skills Practice

Name Date 9. f( ) ( ) 3 f( ) ( 8 96) 3 f( ) 8 96 3 f( ) 8 99 0. f( ) 5 ( ) 0 f( ) 5( 8 6) 0 f( ) 5 0 80 0 f( ) 5 0 00 Convert each quadratic function from standard form to verte form.. f( ) Ais of smmetr: b a ( ) f( ) () () 8 Verte: (, ) Verte form: f( ) ( ). f( ) 8 Ais of smmetr: b a 8 f( ) ( ) 8( ) 6 3 0 Verte: (, 0) Verte form: f( ) ( ) 0 3. f( ) 7 0 Ais of smmetr: b a ( ) f( ) 7 () () 0 7 0 3 Verte: (, 3) Verte form: f( ) 7 ( ) 3 Chapter l Skills Practice 87

. f( ) 8 Ais of smmetr: b a ( ) 3 f( ) ( 3) ( 3) 8 (9) 36 8 8 36 8 6 Verte: ( 3, 6) Verte form: f( ) ( 3) 6 5. f( ) Ais of smmetr: b a 8 ) f( ) ( ) ( ) ( Verte: (, ) Verte form: f( ) ( ) 6. f( ) 6 Ais of smmetr: b a 6 3 ) f( ) ( 3 ) 6 ( 3 ) ( 9 Verte: ( 3, 5 ) Verte form: f( ) ( 3 ) 5 8 9 8 9 5 88 Chapter l Skills Practice

Skills Practice Skills Practice for Lesson.7 Name Date Graphing Quadratic Functions Basic Functions and Transformations Vocabular Match each term with the graph that represents it.. translation. dilation 3. reflection. basic quadratic function Graph D Graph B Graph C Graph A A 0 8 B 0 8 6 6 0 0 6 8 0 0 0 6 8 0 0 0 0 C 0 8 6 0 6 8 0 0 D 0 8 6 0 6 8 0 0 0 Chapter l Skills Practice 89

Problem Set For each quadratic function, describe (without graphing) how the equation and the graph have been transformed from the basic function.. The graph of the basic function was dilated b a factor of.. The graph of the basic function was dilated b a factor of. 3. 5 The graph of the basic function was shifted up 5 units.. 8 The graph of the basic function was shifted down 8 units. 5. ( 3) The graph of the basic function was shifted right 3 units. 6. ( 6) The graph of the basic function was shifted left 6 units. 7. ( ) The graph of the basic function was reflected about the ais. 8. ( ) 3 The graph of the basic function was shifted up 3 units and shifted right units. 90 Chapter l Skills Practice

Name Date Determine the verte of each function. Use the verte and our knowledge of the shape determined b the value of a to graph the function. Then describe the graphical transformations that were used to transform the basic quadratic function to each given function. 9. ( 3) 0 Verte: (3, ) The graph of the basic function is shifted down unit and right 3 units. 8 6 0 0 6 8 0 0 0. ( ) 5 Verte: (, 5) The graph of the basic function is shifted up 5 units and left unit. 6 0 8 6 0 0 6 8 0 Chapter l Skills Practice 9

. ( ) 0 Verte: (, 0) The graph of the basic function is shifted right units and reflected over the -ais. 8 6 0 0 6 8 0 0. 3 0 Verte: (0, 3) The graph of the basic function is shifted up 3 units and reflected over the -ais. 8 6 0 0 6 8 0 3. 0 Verte: (, 6) Ais of smmetr: b a ( ) f( ) () () 8 6 The graph of the basic function is shifted down 6 units and right units. 0 0 8 6 0 6 8 0 0 9 Chapter l Skills Practice

Name Date. 8 0 Verte: (, ) 8 Ais of smmetr: b a 8 f( ) ( ) 8( ) 6 3 The graph of the basic function is shifted down units and left units. 0 6 0 6 8 0 0 5. ( ) 0 Verte: (, 0) 8 The graph of the basic function is shifted left units and dilated b a factor of. 6 0 0 6 8 0 6. 3 8 Verte: (0, 3) The graph of the basic function is shifted up 3 units and dilated b a factor of. 0 7 6 5 3 5 3 0 3 5 Chapter l Skills Practice 93

9 Chapter l Skills Practice