## Calculus 10th Edition

Published by Brooks Cole

# Chapter P - P.1 - Graphs and Models - Exercises: 48

#### Answer

$x$-intercept:$-4$ $y$-intercepts:$\pm2$ This equation is only symmetric with respect to the $x$-axis. The graph is shown below:

#### Work Step by Step

$x=y^{2}-4$ To find the $x$-intercept, let $y$ be equal to $0$ and solve for $x$: $x=(0)^{2}-4$ $x=-4$ To find the $y$-intercept, let $x$ be equal to $0$ and solve for $y$: $y^{2}-4=0$ $y^{2}=4$ $\sqrt{y^{2}}=\sqrt{4}$ $y=\pm2$ Test for symmetry: Substitute $x$ with $-x$ and simplify: $-x=y^{2}-4$ The substitution doesn't yield an equivalent equation, so it isn't symmetric with respect to the $y$-axis Substitute $y$ with $-y$ and simplify: $x=(-y)^{2}-4$ $x=y^{2}-4$ The substitution yields an equivalent equation, so it is symmetric with respect to the $x$-axis Substitute $x$ with $-x$ and $y$ with $-y$ and simplify: $-x=(-y)^{2}-4$ $-x=y^{2}-4$ The substitution doesn't yield an equivalent equation, so it isn't symmetric with respect to the origin. The graph of the equation is shown below:

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