Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 8 - Section 8.5 - Graphs of Quadratic Functions - 8.5 Exercises: 16


opens down and narrower

Work Step by Step

$\bf{\text{Solution Outline:}}$ To identify the opening of the given quadratic function, $ f(x)=-2x^2 ,$ compare $a$ with $0$. If $a$ is greater than $0,$ the graph opens up. Otherwise, it opens down. To determine if the graph is wider, narrower, or the same shape as the graph of $f(x)=x^2,$ compare $|a|$ with $1.$ If it is less than $1,$ the graph is wider. If is greater than $1,$ the graph is narrower. If it is equal to $1,$ then the graph has the same shape. $\bf{\text{Solution Details:}}$ In the given function, the value of $a$ is $a= -2 .$ Since $a \lt0 ,$ then the graph opens $\text{ down .}$ In the given function, the value of $|a|$ is $|a|= 2 .$ Since $|a| \gt1 ,$ then the graph is $\text{ narrower }$ than the graph of $f(x)=x^2.$ Hence, the given function has a parabola that $\text{ opens down and narrower }$ than $f(x)=x^2.$
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