Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 3 - Linear and Quadratic Functions - 3.3 Quadratic Functions and Their Properties - 3.3 Assess Your Understanding - Page 145: 29


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Work Step by Step

We are given the function: $f(x)=-x^2-2x$ Rewrite the function building the square: $f(x)=-(x^2+2x+1)+1=-(x+1)^2+1$ We start by graphing the parent function $a(x)=x^2$. Then horizontally shift $a(x)$ one unit to the left to get $b(x)=(x+1)^2$. Then reflect $b(x)$ across the $x$-axis to get $c(x)=-(x+1)^2$. Finally, vertically shift $c(x)$ one unit upward to get $f(x)=-(x+1)^2+1$.
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