Explanation Given: The quadratic equation is: p ( x ) = − x 2 + 8 x − 12 . Formula used: If a function is f ( x ) = a x 2 + b x + c . Then, (1) The vertex occurs at ( − b 2 a , f ( − b 2 a ) ) . (2) The y -intercept is at ( 0 , f ( 0 ) ) . (3) The x -intercept occurs where f ( x ) = 0 . Calculation: Consider the provided function, p ( x ) = − x 2 + 8 x − 12 Since, a = − 1 , b = 8 , and c = − 12 . So, the vertex occurs at x = − b 2 a . Then, x = − 8 2 ( − 1 ) = 4 To find the y -coordinate, calculate p ( 4 ) . p ( 4 ) = − ( 4 ) 2 + 8 ( 4 ) − 12 = − 16 + 32 − 12 = 4 Therefore, the vertex is at ( 4 , 4 ) . To find the y -intercept, calculate p ( 0 ) . p ( 0 ) = − 0 2 + 8 ( 0 ) − 12 = − 12 Therefore, the y -intercept is ( 0 , − 12 )

MYLAB MATH FOR INTERMEDIATE ALGEBRA 18WK

8th Edition

ISBN: 9780136418306

Author: Tobey

Publisher: PEARSON

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Chapter 8.5, Problem 15E

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To calculate: The vertex, the y-intercept, and x-intercepts of the following function p(x)=−x2+8x−12 and graph the function.

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Chapter 8.5, Problem 14E

Chapter 8.5, Problem 16E

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MYLAB MATH FOR INTERMEDIATE ALGEBRA 18WK

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The vertex, the y -intercept, and x -intercepts of the following function p ( x ) = − x 2 + 8 x − 12 and graph the function.

Solution Summary: The author calculates the vertex, the y -intercept, and x intercepts of the following function and graphs it.

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To calculate: The vertex, the y-intercept, and x-intercepts of the following function p(x)=−x2+8x−12 and graph the function.

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Chapter 8 Solutions