Functions Modeling Change: A Preparation for Calculus, 5th Edition

Published by Wiley
ISBN 10: 1118583191
ISBN 13: 978-1-11858-319-7

Chapter 3 - Quadratic Functions - 3.2 The Vertex of a Parabola - Exercises and Problems for Section 3.2 - Skill Refresher - Page 127: S6

Answer

$$n=6,\:n=-3$$

Work Step by Step

Completing the square, we find: $$n^2-3n-18+\left(-\frac{3}{2}\right)^2-\left(-\frac{3}{2}\right)^2 \\ \left(n-\frac{3}{2}\right)^2-\frac{81}{4}$$ Setting this equal to zero: $$\left(n-\frac{3}{2}\right)^2=\frac{81}{4} \\ n=6,\:n=-3$$
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