Explanation Given: The quadratic equation is: r ( x ) = − 3 x 2 + 6 x − 4 . 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, r ( x ) = − 3 x 2 + 6 x − 4 Since, a = − 3 , b = 6 , and c = − 4 . So, the vertex occurs at x = − b 2 a . Then, x = − 6 2 ( − 3 ) = 1 To find the y -coordinate, calculate r ( 1 ) . r ( 1 ) = − 3 ( 1 ) 2 + 6 ( 1 ) − 4 = − 3 + 6 − 4 = − 1 Therefore, the vertex is at ( 1 , − 1 ) . To find the y -intercept, calculate r ( 0 ) . r ( 0 ) = − 3 ( 0 ) 2 + 6 ( 0 ) − 4 = − 4 Therefore, the y -intercept is ( 0 , − 4 )

Intermediate Algebra Books a la Carte Edition PLUS MyLab Math (8th Edition)

8th Edition

ISBN: 9780134578507

Author: John Tobey Jr., Jeffrey Slater, Jenny Crawford, Jamie Blair

Publisher: PEARSON

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Chapter 8.5, Problem 18E

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To calculate: The vertex, the y-intercept, and x-intercepts of the following function r(x)=−3x2+6x−4 and graph the function.

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Chapter 8.5, Problem 17E

Chapter 8.5, Problem 19E

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The vertex, the y -intercept, and x -intercepts of the following function r ( x ) = − 3 x 2 + 6 x − 4 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 r(x)=−3x2+6x−4 and graph the function.

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Chapter 8 Solutions