Explanation Given Information: The quadratic equation is y = − x 2 + 4 x − 5 . Graph: Consider the provided equation: y = − x 2 + 4 x − 5 …… (1) Compare the equation (1) with standard equation of quadratic equation y = a x 2 + b x + c . Here, a , b and c are the real number and a ≠ 0 . a = − 1 , b = 4 , and c = − 5 . Calculate the value of ( b 2 a ) 2 by substituting a = − 1 , b = 4 , and c = − 5 . ( b 2 a ) 2 = ( 4 2 ( − 1 ) ) 2 = ( − 2 ) 2 = 4 Use the complete square method to write the equation into complete square form. Add and subtract by 4 in equation (1). This equation can be written as, y = ( − x 2 + 4 x − 5 ) + 4 − 4 = ( − x 2 + 4 x − 4 ) + 4 − 5 = − ( x 2 − 4 x + 4 ) − 1 = − ( x − 2 ) 2 − 1 …… (2) Calculate the vertex of the equation y = − ( x − 2 ) 2 − 1 by comparing with the equivalent equation of parabola that is y = a ( x − h ) 2 + k . Here, a is the coefficient of x 2 and vertex is ( h , k ) . The vertex is ( h , k ) = ( 2 , − 1 ) . Calculate the other points by substituting of y accordingly in equation (2). For first ordered pair, substitute x = − 1 in the equation (2). y = − ( − 1 − 2 ) 2 − 1 = − ( − 3 ) 2 − 1 = − 9 − 1 = − 10 Thus, the first ordered pair is ( − 1 , − 10 )

Intermediate Algebra, Books a la Carte Edition, Plus MyLab Math -- Access Card Package (13th Edition)

13th Edition

ISBN: 9780134679884

Author: Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

Publisher: PEARSON

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Chapter 9.1, Problem 5ES

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To graph: The quadratic equation y=−x2+4x−5.

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Chapter 9.1, Problem 4ES

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Chapter 9 Solutions

Intermediate Algebra, Books a la Carte Edition, Plus MyLab Math -- Access Card Package (13th Edition)

Ch. 9.1 - Prob. 1SR Ch. 9.1 - Prob. 2SR Ch. 9.1 - Prob. 1DE Ch. 9.1 - Prob. 2DE Ch. 9.1 - Prob. 1CCE Ch. 9.1 - Prob. 2CCE Ch. 9.1 - Prob. 3CCE Ch. 9.1 - Prob. 3DE Ch. 9.1 - Prob. 4DE Ch. 9.1 - Prob. 5DE

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To graph: The quadratic equation y = − x 2 + 4 x − 5 .

Solution Summary: The author analyzes the quadratic equation y=-x2+4x-5 by comparing it with the standard equation.

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To graph: The quadratic equation y=−x2+4x−5.

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Chapter 9 Solutions