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

4th Edition

ISBN: 9781319434526

Author: Rogawski

Publisher: MAC HIGHER

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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 62E

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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 1.2, Problem 61E

Chapter 1.2, Problem 63E

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Chapter 1 Solutions

CALCULUS 4E (LL) W/ ACHIEVE ACCESS

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

Ch. 1.1 - Prob. 1E Ch. 1.1 - Prob. 2E Ch. 1.1 - Prob. 3E Ch. 1.1 - Prob. 4E Ch. 1.1 - Prob. 5E Ch. 1.1 - Prob. 6E Ch. 1.1 - Prob. 7E Ch. 1.1 - Prob. 8E Ch. 1.1 - Prob. 9E Ch. 1.1 - Prob. 10E Ch. 1.1 - Prob. 11E Ch. 1.1 - Prob. 12E Ch. 1.1 - Prob. 13E Ch. 1.1 - Prob. 14E Ch. 1.1 - Prob. 15E Ch. 1.1 - Prob. 16E Ch. 1.1 - Prob. 17E Ch. 1.1 - Prob. 18E Ch. 1.1 - Prob. 19E Ch. 1.1 - Prob. 20E Ch. 1.1 - Prob. 21E Ch. 1.1 - Prob. 22E Ch. 1.1 - Prob. 23E Ch. 1.1 - Prob. 24E Ch. 1.1 - Prob. 25E Ch. 1.1 - Prob. 26E Ch. 1.1 - Prob. 27E Ch. 1.1 - Prob. 28E Ch. 1.1 - Prob. 29E Ch. 1.1 - Prob. 30E Ch. 1.1 - Prob. 31E Ch. 1.1 - Prob. 32E Ch. 1.1 - Prob. 33E Ch. 1.1 - Prob. 34E Ch. 1.1 - Prob. 35E Ch. 1.1 - Prob. 36E Ch. 1.1 - Prob. 37E Ch. 1.1 - Prob. 38E Ch. 1.1 - Prob. 39E Ch. 1.1 - Prob. 40E Ch. 1.1 - Prob. 41E Ch. 1.1 - Prob. 42E Ch. 1.1 - Prob. 43E Ch. 1.1 - Prob. 44E Ch. 1.1 - Prob. 45E Ch. 1.1 - Prob. 46E Ch. 1.1 - Prob. 47E Ch. 1.1 - Prob. 48E Ch. 1.1 - Prob. 49E Ch. 1.1 - Prob. 50E Ch. 1.1 - 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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