Explanation Given information: An equation of parabola is given as, y = a x 2 − 1 . Also, a changes from − ∞ to ∞ . Concepts used: 1. ) A standard quadratic equation y = a x 2 + b x + c , a ≠ 0 , represents a parabola and the solution of this quadratic is the point where parabola crosses x − axis. 2. ) If a > 0 then, parabola y = a x 2 + b x + c opens upward. 3. ) If a < 0 then, parabola y = a x 2 + b x + c opens downward. Calculation: An equation of parabola is given as, y = a x 2 − 1 . Solution of this quadratic equation will be given as, x = − b ± b 2 − 4 a c 2 a ⇒ x = − 0 ± 0 2 − 4 a

4th Edition

ISBN: 9781319050733

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 7PQ

To determine

How the parabolas y=ax2−1 changes as a changes from −∞ to ∞ .

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Chapter 1.2, Problem 6PQ

Chapter 1.2, Problem 8PQ

Chapter 1 Solutions

CALCULUS (CLOTH)

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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How the parabolas y = a x 2 − 1 changes as a changes from − ∞ to ∞ .

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How the parabolas y=ax2−1 changes as a changes from −∞ to ∞ .

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Chapter 1 Solutions