Explanation Given Information: The given function is 1 2 x 2 + x − y = 3 . Formula used: The vertex of the function y = a x 2 + b x + c is ( − b 2 a , f ( − b 2 a ) ) . For the function y = f ( x ) = a x 2 + b x + c , the solutions of the equation a x 2 + b x + c = 0 are the zeroes. To get the zeroes use the quadratic formula x = − b ± b 2 − 4 a c 2 a . The y -intercept of the function y = a x 2 + b x + c is y = c . Explanation: Rewrite the function as: y = 1 2 x 2 + x − 3 To find the vertex of the function y = 1 2 x 2 + x − 3 is maximum or minimum, compare y = 1 2 x 2 + x − 3 with the function y = a x 2 + b x + c to get a , b and c . a = 1 2 , b = 1 , c = − 3 To find the x -coordinates of the vertex, substitute 1 2 for a and 1 for b in − b 2 a . x = − 1 2 × 1 2 = − 1 1 = − 1 To get the y -coordinates of the vertex, substitute − 1 for x in y = f ( x ) = 1 2 x 2 + x − 3 . y = f ( − 1 ) = 1 2 × ( − 1 ) 2 + ( − 1 ) − 3 = 1 2 − 1 − 3 = 1 − 8 2 = − 7 2 = − 3.5 Therefore, the vertex of the function y = 1 2 x 2 + x − 3 is ( − 1 , − 3

Mathematical Applications for the Management, Life, and Social Sciences

12th Edition

ISBN: 9781337625340

Author: Ronald J. Harshbarger, James J. Reynolds

Publisher: Cengage Learning

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Chapter 2.2, Problem 11E

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Whether the vertex is maximum or minimum, the coordinates of the vertex, the zeroes, the y-intercept, the graph of the function 12x2+x−y=3.

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Chapter 2.2, Problem 10E

Chapter 2.2, Problem 12E

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Whether the vertex is maximum or minimum, the coordinates of the vertex, the zeroes, the y -intercept, the graph of the function 1 2 x 2 + x − y = 3 .

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Whether the vertex is maximum or minimum, the coordinates of the vertex, the zeroes, the y-intercept, the graph of the function 12x2+x−y=3.

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