Explanation Result used: The vertex and the y -intercept of the quadratic function y = a x 2 + b x + c is ( − b 2 a , f ( − b 2 a ) ) and ( 0 , c ) . Description: Compare the equation y = − 2 x 2 − 2 x − 6 with the general quadratic equation . y = a ↓ x 2 + b ↓ x + c ↓ y = − 2 x 2 − 2 x − 6 From the above, the value of a , b and c are observed to be −2, −2 and −6, respectively. Compute the vertex as follows. Obtain the value of x -coordinate in ( − b 2 a , f ( − b 2 a ) ) . Substitute a = − 2 and b = − 2 in − b 2 a . − b 2 a = − ( − 2 ) 2 ( − 2 ) = 2 − 4 = − 1 2 Thus, the x -coordinate of the vertex is − 1 2 . Substitute x = − 1 2 in y = − 2 x 2 − 2 x − 6 and obtain the value of y -coordinate. y = − 2 ( − 1 2 ) 2 − 2 ( − 1 2 ) − 6 = − 1 2 − 5 = − 1 − 10 2 = − 11 2 Thus, the y -coordinate of the vertex is − 11 2 . So, the vertex is ( − 1 2 , − 11 2 ) . Since a < 0 , it can be concluded that the vertex is the maximum point on the graph of the function y = − 2 x 2 − 2 x − 6

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ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Chapter 7.4, Problem 15E

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To sketch: The graph of the function y=−2x2−2x−6 using the vertex, y-intercept and the other two points.

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Chapter 7.4, Problem 14E

Chapter 7.4, Problem 16E

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The graph of the function y = − 2 x 2 − 2 x − 6 using the vertex, y -intercept and the other two points.

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To sketch: The graph of the function y=−2x2−2x−6 using the vertex, y-intercept and the other two points.

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Chapter 7 Solutions