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

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ISBN: 9781319055844

Author: FRANZOSA

Publisher: VST

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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

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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

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Chapter 1 Solutions

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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