Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 1 - Precalculus Review - 1.2 Linear and Quadratic Functions - Exercises - Page 19: 40


$ y=-9$ is the minimum, when $ x=1$

Work Step by Step

Given $$ y= 2 x^{2}-4 x-7 $$ So, we have \begin{aligned} y&=2 x^{2}-4 x-7 \\ &=2\left(x^{2}-2 x\right)-7\\ & =2\left(x^{2}-2 x+1-1\right)-7\\ & =2\left((x-1)(x-1)-1\right)-7\\ & =2\left((x-1)^2-1\right)-7\\ & =2(x-1)^2-9\\ \end{aligned} The lowest value for the squared term is $0$. So, we see that $y=-9$ is the minimum, when $x=1$.
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