Answer
See the graph
Work Step by Step
We are given: $y=\frac{1}{2}x^2$
Make a table of values
$x=-4 \rightarrow y=8$
$x=-2 \rightarrow y=2$
$x=0 \rightarrow y=0$
$x=2 \rightarrow y=2$
$x=4 \rightarrow y=8$
The vertex is $(0,0)$. It is a minimum.