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:
