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: 32


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Work Step by Step

We are given the function: $f(x)=\dfrac{2}{3}x^2+\dfrac{4}{3}x-1$ Rewrite the function building the square: $f(x)=\dfrac{2}{3}(x^2+2x+1)-\dfrac{2}{3}-1=\dfrac{2}{3}(x+1)^2-\dfrac{5}{3}$ We start graphing the parent function $a(x)=x^2$. Then horizontally shift $a(x)$ one unit to the left to get $b(x)=\left(x+1\right)^2$. Then vertically compress $b(x)$ by a factor of $\dfrac{1}{2}$ to get $c(x)=\dfrac{1}{2}\left(x+1\right)^2$. Finally vertically shift $c(x)$ $\dfrac{3}{2}$ units downward to get $f(x)=\dfrac{1}{2}\left(x+1\right)^2-\dfrac{3}{2}$.
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