Answer
Intercepts: $(-1,0), (1,0), (0,-2)$, and $(0,2)$.
The graph has x-axis, y-axis, and origin symmetry.
Work Step by Step
$\left[\begin{array}{ll}
\text{x-intercepts:} & \text{y-intercepts:}\\
4x^{2}+0^{2}=4 & 4(0)^{2}+y^{2}=4\\
4x^{2}=4 & y^{2}=4\\
x^{2}=1 & y=\pm 2\\
x=\pm 1 &
\end{array}\right]$
Intercepts: $(-1,0), (1,0), (0,-2)$, and $(0,2)$.
Test x-axis symmetry: Replace $y$ with $-y$
$4x^{2}+(-y)^{2}=4$
$4x^{2}+y^{2}=4$ ...same as initial equation
Test y-axis symmetry: Replace $x$ with $-x$
$4 (-x)^{2}+y^{2}=4$
$4x^{2}+y^{2}=4$ ...same as initial equation
Test origin symmetry: $x\rightarrow-x$ and $y\rightarrow-y$.
$4 (-x)^{2}+y^{2}=4$
$4x^{2}+y^{2}=4$ ...same as initial equation