Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 2 - Nonlinear Functions - 2.2 Quadratic Functions; Translation and Reflection - 2.2 Exercises: 10

Answer

$\left(\displaystyle \frac{5}{2}, -32\right)$

Work Step by Step

$ f(x)=a(x-h)^{2}+k^{2},\qquad$ vertex: (h,k) (solved as in example 4) $(A\pm B)^{2}=A^{2}\pm 2AB+B^{2}$ ----------- $y=4x^{2}-20x-7$ $=4(x^{2}-5x)-7$ $=4(x^{2}-2\displaystyle \cdot\frac{5}{2}\cdot x+\frac{25}{4}-\frac{25}{4})-7$ $=4(x-\displaystyle \frac{5}{2})^{2}-7-4(\frac{25}{4})$ $=4(x-\displaystyle \frac{5}{2})^{2}-32$ Vertex: $\left(\displaystyle \frac{5}{2}, -32\right)$.
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