Answer
See the graph
Work Step by Step
We are given:
$y=-4x^2$
Make a table of values.
$x=-1 \rightarrow y=-4$
$x=0 \rightarrow y=0$
$x=1 \rightarrow y=-4$
The vertex is $(0,0)$. It is a maximum.
The domain is all real numbers. The range is $y \leq 0$.