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Holt CA Course Graphing Quadratic Functions Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview

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Holt CA Course Graphing Quadratic Functions 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 – y = 1.6x –3, 21, –33 –12, 3.2, –31 5.9, 12.3, –2.1

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Holt CA Course Graphing Quadratic Functions AF3.1 Graph functions of the form y = nx 2 and y = nx 3 and use in solving problems. California Standards

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Holt CA Course Graphing Quadratic Functions Vocabulary quadratic function parabola

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Holt CA Course Graphing Quadratic Functions A quadratic function is a function in which the greatest power of the variable is 2. The most basic quadratic function is y = nx 2 where n 0. The graphs of all quadratic functions have the same basic shape, called a parabola.

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Holt CA Course Graphing Quadratic Functions Create a table for each quadratic function, and use it to graph the function. A. y = x Additional Example 1: Graphing Quadratic Functions Plot the points and connect them with a smooth curve. x x y –2–2 –1– (–2) (–1) (0) (1) (2)

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Holt CA Course Graphing Quadratic Functions B. y = x 2 – x + 1 Additional Example 1: Graphing Quadratic Functions Plot the points and connect them with a smooth curve. x x 2 – x + 1 y –2–2 –1– (–2) 2 – (–2) (–1) 2 – (–1) (0) 2 – (0) (1) 2 – (1) (2) 2 – (2) + 1 3

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Holt CA Course Graphing Quadratic Functions A. y = x 2 – 1 Check It Out! Example 1 Plot the points and connect them with a smooth curve. x x 2 – 1 y –2–2 –1– (–2) 2 – 1 3 (–1) 2 – 1 0 (0) 2 – 1 –1 (1) 2 – 1 0 (2) 2 – 1 3 Create a table for each quadratic function, and use it to make a graph.

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Holt CA Course Graphing Quadratic Functions B. y = x 2 + x + 1 Check It Out! Example 1 Plot the points and connect them with a smooth curve. xx 2 + x + 1 y –2–2 –1– (–2) 2 + (–2) (–1) 2 + (–1) (0) 2 + (0) (1) 2 + (1) (2) 2 + (2) + 1 7

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Holt CA Course Graphing Quadratic Functions A reflecting surface of a television antenna was formed by rotating the parabola y = 0.1x 2 about its axis of symmetry. If the antenna has a diameter of 4 feet, about how much higher are the sides than the center? Additional Example 2: Application

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Holt CA Course Graphing Quadratic Functions Additional Example 2 Continued First, create a table of values. Then graph the cross section. 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. y = 0.1x 2 y 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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Holt CA Course Graphing Quadratic Functions A reflecting surface of a radio antenna was formed by rotating the parabola y = x 2 – 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? Check It Out! Example 2

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Holt CA Course Graphing Quadratic Functions Check It Out! Example 2 Continued xx 2 – x + 2 y (–1) 2 – (–1) (0) 2 – (0) (1) 2 – (1) (2) 2 – (2) First, create a table of values and graph the cross section. 3 ft. 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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Holt CA Course Graphing Quadratic Functions Lesson Quiz: Part I Create a table for the quadratic function, and use it to make a graph. 1. y = x 2 – 2

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Holt CA Course Graphing Quadratic Functions Lesson Quiz: Part II Create a table for each quadratic function, and use it to make a graph. 2. y = x 2 + x – 6

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Holt CA Course Graphing Quadratic Functions Lesson Quiz: Part III 3. The function y = 40t – 5t 2 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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