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Preview Warm Up California Standards Lesson Presentation

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Warm Up For each function, find the value of y for x = 0, x = 4, and x = –5. 1. y = 6x – 3 2. y = 3.8x – 12 3. y = 1.6x + 5.9 –3, 21, –33 –12, 3.2, –31 5.9, 12.3, –2.1

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**Standards California AF3.1 Graph functions of the form**

y = nx2 and y = nx3 and use in solving problems. California Standards

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Vocabulary quadratic function parabola

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A quadratic function is a function in which the greatest power of the variable is 2. The most basic quadratic function is y = nx2 where n ≠ 0. The graphs of all quadratic functions have the same basic shape, called a parabola.

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**Additional Example 1: Graphing Quadratic Functions**

Create a table for each quadratic function, and use it to graph the function. A. y = x2 + 1 Plot the points and connect them with a smooth curve. x x y –2 –1 1 2 (–2) (–1) (0) (1) (2)

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**Additional Example 1: Graphing Quadratic Functions**

Plot the points and connect them with a smooth curve. B. y = x2 – x + 1 x x2 – x y –2 –1 1 2 (–2)2 – (–2) (–1)2 – (–1) (0)2 – (0) (1)2 – (1) (2)2 – (2)

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Check It Out! Example 1 Create a table for each quadratic function, and use it to make a graph. A. y = x2 – 1 Plot the points and connect them with a smooth curve. x x2 – y –2 –1 1 2 (–2)2 – (–1)2 – (0)2 – –1 (1)2 – (2)2 –

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**Plot the points and connect them with a smooth curve. **

Check It Out! Example 1 Plot the points and connect them with a smooth curve. B. y = x2 + x + 1 x x2 + x y –2 –1 1 2 (–2)2 + (–2) (–1)2 + (–1) (0)2 + (0) (1)2 + (1) (2)2 + (2)

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**Additional Example 2: Application**

A reflecting surface of a television antenna was formed by rotating the parabola y = 0.1x2 about its axis of symmetry. If the antenna has a diameter of 4 feet, about how much higher are the sides than the center?

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**Additional Example 2 Continued**

First, create a table of values. Then graph the cross section. y = 0.1x2 y The center of the antenna is at x = 0 and the height is 0 ft. If the diameter of the mirror is 4 ft, the highest point on the sides are at x = 2 and x = –2. The height of the sides at x = 0.1(2)2 = 0.4 ft. The sides are 0.4 ft higher than the center.

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Check It Out! Example 2 A reflecting surface of a radio antenna was formed by rotating the parabola y = x2 – x + 2 about its axis of symmetry. If the antenna has a diameter of 3 feet, about how much higher are the sides than the center?

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**Check It Out! Example 2 Continued**

First, create a table of values and graph the cross section. 3 ft. x x2 – x y -1 1 2 (–1)2 – (–1) (0)2 – (0) (1)2 – (1) (2)2 – (2) The center of the antenna is at x = 0 and the height is 2 ft. If the diameter of the antenna is 3 ft, the highest point on the sides are at x = 2. The height of the antenna at x = (2)2 – (2) + 2 = 4 ft – 2 ft = 2 ft. The sides are 2 ft higher than the center.

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Lesson Quiz: Part I Create a table for the quadratic function, and use it to make a graph. 1. y = x2 – 2

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Lesson Quiz: Part II Create a table for each quadratic function, and use it to make a graph. 2. y = x2 + x – 6

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Lesson Quiz: Part III 3. The function y = 40t – 5t2 gives the height of an arrow in meters t seconds after it is shot upward. What is the height of the arrow after 5 seconds? 75 m

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