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

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1 Lesson.1 Assignment Name Date Shape and Structure Forms of Quadratic Functions 1. Analze the graph of the quadratic function. a. The standard form of a quadratic function is f() 5 a 1 b 1 c. What possible values can a and c have for the given quadratic function? Eplain our reasoning. b. The verte form of a quadratic function is f() 5 a( h ) 1 k. What possible values can a, h, and k have for the given quadratic function? Eplain our reasoning. c. The factored form of a quadratic function is f() 5 a( r 1 )( r ). What possible values can a, r 1, and r have? Eplain our reasoning.. Write a quadratic function for the parabola that passes through the point (, 3) with roots (, ) and (, ). Chapter Assignments 17

2 Lesson.1 Assignment page 3. Mitzu shoots an arrow from an initial height of meters. The arrow reaches its maimum height of meters after it has flown a distance of meters. a. Write a quadratic function to represent the height of the arrow as a function of its distance. b. Determine the height of the arrow after it has flown a distance of 1 meters.. Charlie kicks a soccer ball from the ground through a hoop that is feet awa at a height of feet. The ball hits the ground 1 feet from where Charlie kicked it. a. Write a quadratic function to represent the height of the ball as a function of its distance. b. Determine the maimum height of the ball during its flight. 1 Chapter Assignments

3 Lesson. Assignment Name Date Function Sense Translating Functions 1. Graph d() 5 ( 1 3 ) 1 without a calculator. Eplain each of our steps.. Graph g() 5 ( 5 ) without a calculator. Eplain each of our steps. Chapter Assignments 19

4 Lesson. Assignment page 3. The function h() is shown. If f() 5, write h() in terms of f(). 1 (9, ) (, 1) (7, ) 1. The function p() is shown. If f() 5, write p() in terms of f(). (, 7) (, 3) (5, ) 5. The function t() is a translation of f() 5, and t() has a verte at (5, 9). Write the function t(). Eplain our reasoning. Chapter Assignments

5 Lesson.3 Assignment Name Date Up and Down Vertical Dilations of Quadratic Functions 1. Graph d() 5 1 ( 1 5) 3 without a calculator. Eplain each of our steps.. Graph g() 5 3( ) without a calculator. Eplain each of our steps. Chapter Assignments 1

6 Lesson.3 Assignment page 3. Write the function h() that represents the given graph. Eplain our reasoning. (5, 7) (, 5) (3, 1). Write the function p() that represents the given graph. Eplain our reasoning. (, ) 1 (, 1) (5, 7) 5. The function t() is a transformation of f() 5. The function t() has a verte at (1, 15) and has been verticall compressed b a factor of 1. Write the function t(). Eplain our reasoning. Chapter Assignments

7 Lesson. Assignment Name Date Side to Side Horizontal Dilations of Quadratic Functions 1. Graph m() 5 ( ) 1 without a calculator. Eplain each of our steps. 1. Write the function p() that represents the given graph. Eplain our reasoning. 1 (3, 9) (9, 5) (, ) Chapter Assignments 3

8 Lesson. Assignment page 3. Graph g() 5 ( ) without a calculator. Eplain each of our steps.. The graph of the quadratic function t() is shown. If f() 5, write t() in terms of f(). Eplain our reasoning. (3, ) (1, 3) (5, ) Chapter Assignments

9 Lesson.5 Assignment Name Date What s the Point? Deriving Quadratic Functions 1. Use our knowledge of reference points to write an equation for the quadratic function that has -intercepts at (1, ) and (1, ) and a -intercept at (, 3).. Use our knowledge of reference points to write an equation for the quadratic function that has a verte at (, 3) and passes through (, 1). 3. Use our knowledge of reference points to write an equation for the quadratic function that has one -intercept at (7, ) and passes through (, 1). Chapter Assignments 5

10 Lesson.5 Assignment page. Create a sstem of equations and use algebra to write a quadratic function that passes through the points (, ), (1, 1), and (, 1). 5. Victoria competes in a discus throwing competition. She needs to throw her discus at least feet to win the event. The discus has an initial height of 5 feet when she releases it. The discus reaches a height of 5 feet after traveling 75 feet and a height of feet after traveling 15 feet. a. Write a quadratic function to model the height of the discus as a function of the distance traveled. b. Does Victoria win the competition? Eplain our reasoning. c. What was the maimum height of the discus? Chapter Assignments

11 Lesson. Assignment Name Date Now It s Getting Comple... But It s Reall Not Difficult! Comple Number Operations 1. Calculate each power of i. a. i b. i 3 c. i 73 d. i. Simplif each epression. Identif the real and imaginar parts of our answer. a. 1 b. 7 Chapter Assignments 7

12 Lesson. Assignment page 3. Solve each equation for. Identif the real and imaginar parts of our answer. a i i b. 5 i 5 1 i. Multipl each number b its comple conjugate. Identif the real and imaginar parts of our answer. a. i b. 5 1 i 5. Simplif the epression (3 1 i )( 1 i )(3 i )( i ). Identif the real and imaginar parts of our answer. Chapter Assignments

13 Lesson.7 Assignment Name Date You Can t Spell Fundamental Theorem of Algebra without F-U-N! Quadratics and Comple Numbers 1. The Internet Bargains Compan models their profit during different -da periods throughout the ear. The function p() represents the dail profit (in thousands of dollars) on the th da of each period. When p()., the compan has a dail profit. When p(),, the compan has a dail loss. a. The model for one -da period is p() 5.( 1 ) 1. Determine which of the das in the -da period the compan made a profit without using a calculator. Eplain our reasoning. b. The model for one -da period is p() 5.1( 3)( 15). Determine which of the das in the -da period the compan made a profit without using a calculator. Eplain our reasoning. c. The model for one -da period is p() 5.( 9 ). Determine which of the das in the -da period the compan made a profit without using a calculator. Eplain our reasoning.. Determine the number of roots for each given equation and whether the roots are real or imaginar. a Chapter Assignments 9

14 Lesson.7 Assignment page b c Write a quadratic equation in standard form with the given roots. a. Write a quadratic equation with a double root of 5. b. Write a quadratic equation with a root of 3 1 i. 3 Chapter Assignments