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Lesson Menu Five-Minute Check (over Lesson 9–7) Then/Now New Vocabulary Key Concept: Quadratic Function Example 1:Graph Quadratic Functions Example 2:Graph Quadratic Functions Example 3:Use Quadratic Functions

Over Lesson 9–7 5-Minute Check 1 A.linear B.nonlinear Does the graph represent a linear or nonlinear function?

Over Lesson 9–7 5-Minute Check 2 A.linear B.nonlinear Does the table represent a linear or nonlinear function?

Over Lesson 9–7 5-Minute Check 3 A.linear B.nonlinear Does 3x + y = –10 represent a linear or nonlinear function?

Over Lesson 9–7 5-Minute Check 4 A.linear B.nonlinear Does y = 2 x represent a linear or nonlinear function?

Over Lesson 9–7 5-Minute Check 5 A.No, it can be written as 600x + y = 50. B.No, dollars and advertising are not related. C.Yes, it can be written as y = 600x D.Yes, the company’s sales went up. A company found that for every dollar x that they spend on advertising, they had sales y of 600x + 50 dollars. Is the relationship between dollars spent of advertising and dollars a linear relationship?

Over Lesson 9–7 5-Minute Check 6 A.y = 16x + 4 B.y = 20x – 4 C.y = 20x – 2 D.y = x 2 – 6 Which equation describes the data in the table?

Then/Now You used linear functions to solve problems. (Lesson 8–7) Graph quadratic equations. Use quadratic functions to solve problems.

Vocabulary quadratic function parabola

Concept

Example 1 Graph Quadratic Functions Graph y = –x 2 – 3. Answer:

Example 1 Graph y = x A.B. C.D.

Example 2 Graph Quadratic Functions Graph y = –2x 2. Make a table of values, plot the ordered pairs, and connect the points with a curve. Answer:

A.B. C.D. Example 2 Graph y = –x 2.

Example 3 Use Quadratic Functions SKYDIVING The distance, d, in feet that a skydiver falls can be found using the equation d = 16t 2. A. Graph this equation and interpret your graph. How far will the skydiver fall in 4.5 seconds? Make a table of values, then plot the ordered pairs.

Example 3 Use Quadratic Functions The graph shows the distance the skydiver falls over a period of about 6 seconds. The distance at 0 seconds is 0 feet, so the skydiver had not yet left the airplane. As the time increases the distance also increases. Answer: From the graph, it appears that the distance the skydiver falls after 4.5 seconds is about 320 feet. Substituting 4.5 for t in the equation d = 16t 2, the distance is 16 ● (4.5) 2 or 324 feet.

Example 3 Use Quadratic Functions SKYDIVING The distance, d, in feet that a skydiver falls can be found using the equation d = 16t 2. B. What values of the domain and range are unreasonable? Explain. Answer: Unreasonable values for x would be any negative numbers because time cannot be negative. Negative values for y are also unreasonable because distance cannot be negative.

Example 3 CYP A. GEOMETRY The length of a rectangle is 3 times its width. Write a formula for the area and graph it. Find the area of the rectangle whose width is 3.5 inches. A.A = 4w; 14 in 2 B.A = w 2 + 3; in 2 C.A = 8w; 28 in 2 D.A = 3w 2 ; in 2

Example 3 CYP B. GEOMETRY The length of a rectangle is 3 times its width. What values of the domain and range are unreasonable? A.negative values for the domain only B.negative values for the range only C.negative values for both the domain and range D.There are no unreasonable values.

End of the Lesson