Explanation Given Information: The given quadratic equation is y = 12 x − 9 − 4 x 2 . …… (1) 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 quadratic function is y = f ( x ) = a x 2 + b x + c . 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. Zero product property: The general form of quadratic equation is a x 2 + b x + c = 0 where a , b , c are constants and a ≠ 0 . For real numbers a and b , a b = 0 if and only if a = 0 or b = 0 or both . Calculation: To find the vertex, first check the value of a . a = − 4 < 0 The graph opens downward and the vertex is the maximum point. Compare the equation (1) with the quadratic function. a = − 4 and b = 12 Use the formula of the vertex ( − b 2 a , f ( − b 2 a ) ) . ( x , y ) = ( − b 2 a , f ( − b 2 a ) ) = ( − 12 2 ( − 4 ) , 12 ( − 12 2 ( − 4 ) ) − 9 − 4 ( − 12 2 ( − 4 ) ) 2 ) = ( 3 2 , 12 ( 3 2 ) − 9 − 4 ( 3 2 ) 2 ) = ( 3 2 , 18 − 9 − 9 ) = ( 1

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ISBN: 9781305713864

Author: HARSHBARGER

Publisher: CENGAGE L

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Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.

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Chapter 2, Problem 24RE

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To calculate: The vertex and determine if it is a maximum or minimum point of the quadratic equation $y=12x−9−4x2$ . Also, find the $y−$ intercept and the zeros and draw the graph.

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Chapter 2, Problem 23RE

Chapter 2, Problem 25RE

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The vertex and determine if it is a maximum or minimum point of the quadratic equation y = 12 x − 9 − 4 x 2 . Also, find the y − intercept and the zeros and draw the graph.

Solution Summary: The author calculates the vertex and determines if it is a maximum or minimum point of the quadratic equation.

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To calculate: The vertex and determine if it is a maximum or minimum point of the quadratic equation $y=12x−9−4x2$ . Also, find the $y−$ intercept and the zeros and draw the graph.

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