1. 5-49. Several parabolas and equations are shown below. Match each graph with its equation. Justify your choices and share any shortcuts you discover with your teammates. (Note: Not every equation has a matching parabola.) a. y = (x + 3) 2 b. y = x 2 + 3x – 28 c. y = x 2 – 11x + 28 d. y = –x 2 + 4 e. y = x 2 + 10x + 24 f. y = 2x 2 + 11x + 5 g. y = x 2 – 4x h. y = (x – 3) 2 i. y = 4x 2 – 4x – 3

2. 5.1.5 COMPLETING THE QUADRATIC WEB January 21, 2016

3. Objectives CO: SWBAT move from the graphs of quadratic functions to writing the equations for parabolas with one or two x- intercepts. LO:SWBAT explain to a customer how to ask for a specific parabola.

4. 5-51. EXTRA! EXTRA! A journalist from the school newspaper wants to publish the results from the water balloon contest. She wants an equation for each launch so that she can program her computer to create a graph for her article. a. Examine the graph at right that represents the height of Jen’s toss. Write an equation for this parabola. b. Al releases his balloon from the 10-yard line, and it lands at the 16-yard line. If the balloon reaches a height of 27 yards, what equation represents the path of his launch? c. The journalist knows that the factored form of a quadratic function is y = a(x – d)(x – f). Explain to the journalist how she can determine the values of a, d, and f to write the equation of a quadratic function in factored form. Give examples.

5. Progress Chart ABC Purple Stripes Blue Green Pink Orange Yellow Red

6. 5-51. EXTRA! EXTRA! A journalist from the school newspaper wants to publish the results from the water balloon contest. She wants an equation for each launch so that she can program her computer to create a graph for her article. a. Examine the graph at right that represents the height of Jen’s toss. Write an equation for this parabola. Use your graphing calculator to check your equation with the graph. y = –2x(x – 8) y = –2x 2 + 16x b. Al releases his balloon from the 10-yard line, and it lands at the 16-yard line. If the balloon reaches a height of 27 yards, what equation represents the path of his launch? y = –3(x – 10)(x – 16) y = -3(x 2 - 26x + 160) y = -3x 2 + 78x + 480 c. The journalist knows that the factored form of a quadratic function is y = a(x – d)(x – f). Explain to the journalist how she can determine the values of a, d, and f to write the equation of a quadratic function in factored form. Give examples. Substitute the x-coordinates of the x-intercepts for d and f. For example, for Jen’s toss, the x-intercepts are 0 and 8, so the equation is y = a(x – 0)(x – 8), or y = ax(x – 8). Then substitute a third point into the equation to solve for a. For examples, the vertex of Jen’s toss is (4, 32), so substitute x = 4 and y = 32 to solve for a: 32 = a(4)(–4), so a = –2.

7. 5-50. QUALITY CONTROL, Part One Congratulations! With your promotion, you are now the Quality Assurance Representative at the Function Factory that makes parabolas for Functions of America. Your job is to make sure your clients are happy. Each parabola is ordered using its equation. Whenever a client writes to the company, you must reply with clear directions that will help the client order a parabola that meets his or her needs. Your boss has provided graphing technology and a team of fellow employees to help you fulfill your job description. 1. Carefully read the complaints below. Use your graphing calculator to study each situation. Work with your team to resolve each situation. 2. Write each customer a friendly response that offers a solution to his or her problem. Remember that the customers are not parabola experts! Do not assume that they know anything about parabolas.

8. Progress Chart ABC Purple Stripes Blue Green Pink Orange Yellow Red

9. 5-50. QUALITY CONTROL, Part One Congratulations! With your promotion, you are now the Quality Assurance Representative at the Function Factory that makes parabolas for Functions of America. Your job is to make sure your clients are happy. Each parabola is ordered using its equation. Whenever a client writes to the company, you must reply with clear directions that will help the client order a parabola that meets his or her needs. Your boss has provided graphing technology and a team of fellow employees to help you fulfill your job description. 1. Carefully read the complaints below. Use your graphing calculator to study each situation. Work with your team to resolve each situation. 2. Write each customer a friendly response that offers a solution to his or her problem. Remember that the customers are not parabola experts! Do not assume that they know anything about parabolas. A: Need a third point; y = a(x – 1)(x + 6) B: y = (x – 5) 2 or y = –(x – 5) 2 C: y = –(x + 3)(x – 2)