a) Explanation Given Information: Consider the function f ( x ) = 3 x 2 − 18 x + 16 . Formula Used: The quadratic equation a x 2 + b x + c = 0 represents a parabola. If a is positive, then parabola opens upward. If a is negative, then parabola opens downward. The vertex of the parabola is ( − b 2 a , f ( − b 2 a ) ) . If a < 0 , then the vertex point is maximum point. If a > 0 , then the vertex point is minimum point. Explanation: Compare the equation (1) with the equation f ( x ) = a x 2 + b x + c , to find the value of a , b and c . a = 3 , b = − 18 , c = 16 To find the x − coordinate, substitute 3 for a and − 18 for b in x = − b 2 a . x = − ( − 18 ) 2 × ( 3 ) = 18 6 = 3 To find the y − coordinate, substitute 3 for x in the equation f ( x ) = 3 x 2 − 18 x + 16 . f ( 3 ) = 3 × 3 2 − ( 18 × 3 ) + 16 = 27 − 54 + 16 = − 11 The vertex is ( 3 , − 11 ) b) To determine To graph: The solutions to f ( x ) = 0 .

Mathematical Applications for the Management, Life, and Social Sciences

11th Edition

ISBN: 9781305108042

Author: Ronald J. Harshbarger, James J. Reynolds

Publisher: Cengage Learning

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Question

Chapter 2.2, Problem 28E

To determine

The vertex of the given function f(x)=3x2−18x+16.

To determine

To graph: The solutions to f(x)=0.

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Chapter 2.2, Problem 27E

Chapter 2.2, Problem 29E

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The vertex of the given function f ( x ) = 3 x 2 − 18 x + 16 .

Solution Summary: The author explains that the vertex of the given function is (3,-11).