Explanation Given info: y = a x 2 y = a x 2 + b x + c Concept used: If y = f ( x ) graph is known then graph of y = f ( x ) + c is obtained by vertical shift of graph y = f ( x ) by c unit above. The graph of y = f ( x − c ) is obtained by shifting the graph of y = f ( x ) in horizontal direction towards the right by C unit. In above transformation graph, shape does not change. Calculation: y = a x 2 + b x + C = a [ x 2 + b a x + c a ] = a [ x 2 + 2 x ( b 2 a ) + ( b 2 a ) 2 - ( b 2 a ) 2 + c a ] = a [ ( x + b 2 a ) 2 + + 4 a c - b 2

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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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 1.2, Problem 60E

To determine

Show by completing the square,that the parabola y=ax2+bx+C is congruent to y=ax2 by a vertical and horizontal translation

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Chapter 1.2, Problem 59E

Chapter 1.2, Problem 61E

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Chapter 1 Solutions

Calculus - Standalone book

Ch. 1.1 - Prob. 1PQ Ch. 1.1 - Prob. 2PQ Ch. 1.1 - Prob. 3PQ Ch. 1.1 - Prob. 4PQ Ch. 1.1 - Prob. 5PQ Ch. 1.1 - Prob. 6PQ Ch. 1.1 - Prob. 7PQ Ch. 1.1 - Prob. 8PQ Ch. 1.1 - Prob. 9PQ Ch. 1.1 - Prob. 10PQ

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Show by completing the square,that the parabola y = a x 2 + b x + C is congruent to y = a x 2 by a vertical and horizontal translation

Solution Summary: The author explains that the parabola y = ax2+bx+c is congruent to y2. The graph is obtained by vertical and horizontal transformation.

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Show by completing the square,that the parabola y=ax2+bx+C is congruent to y=ax2 by a vertical and horizontal translation

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Chapter 1 Solutions