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

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1 - Quadratic Functions and Transformations For Eercises, choose the correct letter.. What is the verte of the function 53()? D (, ) (, ) (, ) (, ). Which is the graph of the function f ()5(3) 5? F 6 6 O 6 6 O 6 O O 6 3. Which of the following best describes how to transform 5 to the graph of 5(.5) 3? C Translate.5 units left, stretch b a factor of, translate 3 units down. Translate 3 units right and.5 units down, stretch b a factor of. Translate.5 units right, stretch b a factor of, translate 3 units down. Stretch b a factor of, translate.5 units left and 3 units down.. What is the equation of the parabola with verte (, 6) passing through the point (, )? I 5() 6 5() 6 5() 6 5() 6 5. A baseball is hit so that its height above ground is given b the equation h56t 96t, where h is the height in feet and t is the time in seconds after it is hit. Show our work. a. How long does it take the baseball to reach its highest point? b. How high will it go? [] a. 3 s; b. 8 ft [] incorrect time to highest point OR incorrect final height OR correct time and distance, but no work shown [0] incorrect answers and no work shown OR no answers given Prentice Hall Algebra Teaching Resources

2 - Standard Form of a Quadratic Function For Eercises 6, choose the correct letter.. What is the verte of the parabola 5 85? B (, ) (, ) (, 5) (, 5). What is the maimum value of the function 53 8? Which function has the graph shown at the right? D What is the verte form of the function 53? F 53() 5 53() 53() 53() 5 F 3 5. What is the equation of the parabola with verte (3, 0) and that passes through the point (, )? B For the function 55 0c, the verte is (, 8). What is c? H To increase revenue, a count wants to increase park fees. The overall income will go up, but there will be epenses involved in collecting the fees. For a p% increase in the fees, this cost C will be C50.6p.p8, in thousands of dollars. What percent increase will minimize the cost to the count? Show our work. b [] 6%; the minimum is at the verte, which is a 5. (0.6) 5 6. [] computational error OR work not shown [0] incorrect answer and no work shown OR no answer given Prentice Hall Algebra Teaching Resources

3 -3 Modeling With Quadratic Functions For Eercises 5, choose the correct letter.. Which parabola passes through the points (, ), (, ), and (5, ) B. Which parabola passes through the points in the table at the right? A baseball coach records the height at ever second of a ball thrown in the air. Some of the data appears in the table below. I f() Time (s) Height (ft) Which equation is a quadratic model for the data? A h56t 80t h53t 80t h58t t h56t 6t. Use the table in Eercise 3. What is the height of the ball at.5 s? 80 ft 00 ft 88 ft ft H 5. Which of the following sets of values cannot be modeled with a quadratic function? (, 3), (0, ), (3, ) (, ), (, 5), (3, ) C f ()5, f ()5, f (0)53 f ()56, f (0)5, f ()53 6. The accountant for a small compan studied the amount spent on advertising and the compan s profit for several ears. He made the table below. What is a quadratic model for the data? Show our work. Advertising (Hundreds of Dollars) Profit (Dollars) [] [] correct method but computational errors OR correct model but no work shown [0] incorrect answers and no work shown OR no answers given Prentice Hall Algebra Teaching Resources

4 - Factoring Quadratic Epressions For Eercises 6, choose the correct letter.. What is the complete factorization of 5? B (5)(3) (3)(5) (3)(5) (5)(3). What is the complete factorization of 38? I ()() ()() ()() ()() 3. What is the complete factorization of 6 96? A 3()() 3()() (3)(3) 3()(). What is the complete factorization of 6 569? G ()() () () 6() 5. What is the complete factorization of 5 0? (5)(5) C 5()() 5()() 5() 6. What is the complete factorization of? I (8)(3) ()() ()(6) ()(). The area in square meters of a rectangular parking lot is The width in meters is 60. What is the length of the parking lot in meters? Show our work. [] 35 [] correct method but an error in finding the length OR correct length but no work shown [0] incorrect answer and no work shown OR no answer given Prentice Hall Algebra Teaching Resources 3

5 -6 Completing the Square For Eercises 6, choose the correct letter.. What are the solutions of the equation 36 5?, 8 6, 6, 6 D 6,. What are the solutions of the equation 6850?!30!!!30 G 3. Which value completes the square for 3? 9 3 A 9 9. Which value for k would make the left side of k a perfect square trinomial? H 5. What are the solutions of the equation 5 8?!!5!5! C 8 6. Which equation is the verte form of 53? G 53() 5 53() 5 53() 5 53() 5. The equation p5 85 gives the price p, in dollars, for a product when million units are produced. a. What are the solutions of the equation 8550? b. What is the positive solution to part (a) rounded to two decimal places? What does this solution mean in terms of this problem? [] a. 6! b. 8.58; the price will be $0 when 8.58 million units are produced. [] incorrect solution OR incorrect interpretation [0] no answers given Prentice Hall Algebra Teaching Resources 5

6 - The Quadratic Formula For Eercises 6, choose the correct letter.. What is the solution of 3 550? Use the Quadratic Formula. A 5 3,, 5 3 3, 5 5, 3. What is the solution of 8350? Use the Quadratic Formula. H!!0!0! 3. What is the solution of 555? Use the Quadratic Formula. 5,, 5 5!5 D 53!5. What is the solution of 5 63? Use the Quadratic Formula. I 3! !6 5. What is the discriminant of the equation 3 50? B 6 3! What is the discriminant of the equation 8950? H Etended Response. The equation d5n n3 models the number of defective items d produced in a manufacturing process when there are n workers in a restricted area. Use the discriminant to answer the following questions. Show our work. a. Will the number of defective items ever be 0? b. Will the number of defective items ever be? c. Will the number of defective items ever be 5? [] a. es; b. es; c. no; the answers are based on the value of the discriminant for each case: (a), (b) 0, and (c) 8. [3] appropriate method with one computational error [] appropriate method with several computational errors [] correct answers but no work shown [0] incorrect answers and no work shown OR no answers given Prentice Hall Algebra Teaching Resources 6

7 -8 Comple Numbers For Eercises 8, choose the correct letter.. What is the simplified form of (8 5i) (3 i)? B 3i 53i i 53i. What is the simplified form of ( 6i) ( i)? I 6i 8i 56i 58i 3. What is the simplified form of (5!36) (!9)? D 93i 985i i 93i. What is the simplified form of (5i)(3i)? G 5i 5 5 5i 5. What is the simplified form of (3 i)( i)? C i 0i 5i 38i 6. What is the simplified form of (83i)? H 3 66i 558i 558i. What is 53i i written as a comple number? 0 0 i i 5 3 i 0 0 i A 8. What are the solutions of ? F 66i i 9. What are the solutions of 3650? Show our work. [] 3 6!39 i; [] quadratic formula properl used, but some computational errors OR correct solutions without work shown [0] incorrect answers and no work shown OR no answers given Prentice Hall Algebra Teaching Resources

8 -9 Quadratic Sstems For Eercises, choose the correct letter.. What is the solution of the sstem? e (0, 5), (, ) (, ), (, 6) (, 0), (, 5) (, 0), (3, ) D. What is the solution of the sstem? e 5 5 (, ), (, 0) (3, 5), (, ) (, ), (, ) (3, ), (, 0) G 3. What is the solution of the sstem? e (, 8), (3, 0) (, 8), (, 3) (, 0), (3, 0) (0, 3), (, ) A. What is the solution of the sstem? e (, ), (, 9) (, 0), (3, 8) (, 0), (, 5) (, ), (, 5) G 5. What is the solution of the sstem? Solve b graphing. e, 3. 6 [] [] an error in graphing one of the functions OR the wrong region is shaded [0] no answer given Prentice Hall Algebra Teaching Resources 8