Answer
Intercepts: $(-4,0), (0,-2)$ and $(0,2)$.
The graph has x-axis symmetry.
Work Step by Step
$y^{2}=x+4$
$\left[\begin{array}{ll}
\text{x-intercepts:} & \text{y-intercepts:}\\
0^{2}=x+4 & y^{2}=0+4\\
-4=x & y^{2}=4\\
& y=\pm 2\\
&
\end{array}\right]$
The intercepts are $(-4,0), (0,-2)$ and $(0,2)$.
Test x-axis symmetry: Replace $y$ with $-y$
$(-y)^{2}=x+4$
$y^{2}=x+4$ ...same as initial equation
Test y-axis symmetry: Replace $x$ with $-x$
$y^{2}=-x+4$ ... different from initial equation
Test origin symmetry: $x\rightarrow-x$ and $y\rightarrow-y$.
$(-y)^{2}=-x+4$
$y^{2}=-x+4$ ... different from initial equation