Precalculus (10th Edition)

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

Chapter 2 - Functions and Their Graphs - 2.5 Graphing Techniques: Transformations - 2.5 Assess Your Understanding - Page 104: 73


$f(x)=-3(x+2)^2-5$ See graph

Work Step by Step

We are given the function: $f(x)=-3x^2-12x-17$ Complete the square: $f(x)=-3(x^2+4x)-17=-3(x^2+4x+4)+12-17=-3(x+2)^2-5$ We start graphing with the basic function $a(x)=x^2$. We horizontally shift $a(x)$ by 2 units to the left to get $b(x)=(x+2)^2$. Then we vertically stretch $b(x)$ by a factor of 3 to get $c(x)=3(x+2)^2$. Then we reflect $c(x)$ about the $x$-axis to get $d(x)=-3(x+2)^2$. Finally we vertically shift $d(x)$ 5 units downward to get $f(x)=-3(x+2)^2-5$. We use 3 points: $(-2,-5),(-3,-8),(-1,-8)$.
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