Explanation Given: The quadratic equation is: f ( x ) = x 2 − 6 x + 5 . 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 + 5 Since, a = 1 , b = − 6 , and c = 5 . 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 ) + 5 = 9 − 18 + 5 = − 4 Therefore, the vertex is at ( 3 , − 4 ) . To find the y -intercept, calculate f ( 0 ) . f ( 0 ) = ( 0 ) 2 − 6 ( 0 ) + 5 = 5 Therefore, the y -intercept is ( 0 , 5 )

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Chapter 8.5, Problem 19E

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To calculate: The vertex, the y-intercept, and the x-intercepts of the following function f(x)=x2−6x+5 and graph the function.

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Chapter 8.5, Problem 18E

Chapter 8.5, Problem 20E

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The vertex, the y -intercept, and the x -intercepts of the following function f ( x ) = x 2 − 6 x + 5 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+5 and graph the function.

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