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: 52


See graph

Work Step by Step

We are given the function: $f(x)=3(x-2)^2+1$ We start graphing with the basic function $a(x)=x^2$. We horizontally shift $a(x)$ by 2 units to the right to get $b(x)=(x-2)^2$. Then we vertically stretch $b(x)$ by a factor of 3 to get $c(x)=3(x-2)^2$. Finally we vertically shift $c(x)$ one unit upward to get $f(x)=3(x-2)^2+1$. We use 3 points: $(1,4),(2,1),(3,4)$.
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