# Chapter 8 - Section 8.5 - Graphs of Quadratic Functions - 8.5 Exercises: 15

opens up and wider

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ To identify the opening of the given quadratic function, $f(x)=-\dfrac{2}{5}x^2 ,$ 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 $a= -\dfrac{2}{5} .$ Since $a \lt0 ,$ then the graph opens $\text{ down .}$ In the given function, the value of $|a|$ is $|a|= \dfrac{2}{5} .$ Since $|a| \lt1 ,$ then the graph is $\text{ wider }$ than the graph of $f(x)=x^2.$ Hence, the given function has a parabola that $\text{ opens up and wider }$ than $f(x)=x^2.$

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