Explanation Given: The graph is shown below: Calculation: The quadratic equation is as follows: y = a x 2 + b x + c The points are ( 2 , 8 ) , ( 4 , 2 ) , a n d ( 6 , 4 ) . The task here is to find the equations in variable a, b and c and solve for the values of a, b , and c . Put x = 2 and y = 8 : 8 = a ( 2 ) 2 + b ( 2 ) + c 8 = 4 a + 2 b + c Put x = 4 and y = 2 : 2 = a ( 4 ) 2 + b ( 4 ) + c 2 = 16 a + 4 b + c Put x = 6 and y = 4 : 4 = a ( 6 ) 2 + b ( 6 ) + c 4 = 36 a + 6 b + c The system of equations in variable a, b and i is as follows: 4 a + 2 b + c = 8 16 a + 4 b + c = 2 36 a + 6 b + c = 4 Mark these equations as follows: 4 a + 2 b + c = 8 Mark it as equation (I) 16 a + 4 b + c = 2 Mark it as equation (II) 36 a + 6 b + c = 4 Mark it as equation (III) Multiply equation (I) by − 4 and eliminate a equations (I) and (III): 16 a + 4 b + c = 2 − 16 a − 8 b − 4 c = − 3 2 _ − 4 b − 3 c = − 30

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ISBN: 9780321837240

Author: Robert F. Blitzer

Publisher: PEARSON

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Maximization

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 8.2, Problem 28E

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To calculate: The equation of the quadratic function y=ax2+bx+c whose graph is as follows:

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Chapter 8.2, Problem 27E

Chapter 8.2, Problem 29E

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The equation of the quadratic function y = a x 2 + b x + c whose graph is as follows:

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To calculate: The equation of the quadratic function y=ax2+bx+c whose graph is as follows:

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