Explanation Given: The quadratic equation is: f ( x ) = x 2 + 6 x + 8 . 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, f ( x ) = x 2 + 6 x + 8 Since, a = 1 , b = 6 , and c = 8 . So, the vertex occurs at x = − b 2 a . Then, x = − 6 2 ( 1 ) = − 3 To find the y -coordinate, calculate f ( − 3 ) . f ( − 3 ) = ( − 3 ) 2 + 6 ( − 3 ) + 8 = 9 − 18 + 8 = − 1 Therefore, the vertex is at ( − 3 , − 1 ) . To find the y -intercept, calculate f ( 0 ) . f ( 0 ) = ( 0 ) 2 + 6 ( 0 ) + 8 = 8 Therefore, the y -intercept is ( 0 , 8 )

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 12E

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To calculate: The vertex, the y-intercept, and the x-intercepts of the following function f(x)=x2+6x+8 and graph the function.

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Chapter 8.5, Problem 11E

Chapter 8.5, Problem 13E

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The vertex, the y -intercept, and the x -intercepts of the following function f ( x ) = x 2 + 6 x + 8 and graph the function.

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

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To calculate: The vertex, the y-intercept, and the x-intercepts of the following function f(x)=x2+6x+8 and graph the function.

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Chapter 8 Solutions