Answer
See the graph
![](https://gradesaver.s3.amazonaws.com/uploads/solution/fc79291c-fa67-454f-9d31-54ca09d01185/result_image/1595156756.png?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T021259Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=1d14bbdf21bce0a33932a11f9e3b4bde7a05c59c826f45d9083917262e793051)
Work Step by Step
We are given: $y=-\frac{1}{3}x^2$
Make a table of values.
$x=-2 \rightarrow y=-\frac{4}{3}$
$x=-1 \rightarrow y=-\frac{1}{3}$
$x=0 \rightarrow y=0$
$x=1 \rightarrow y=-\frac{1}{3}$
$x=2 \rightarrow y=-\frac{4}{3}$
The vertex is $(0,0)$. It is a maximum.
The domain is all real numbers. The range is $y \leq 0$.