Answer
See the graph
Work Step by Step
We are given: $y=1.5x^2$
Make a table of values.
$x=-2 \rightarrow y=6$
$x=-1 \rightarrow y=1.5$
$x=0 \rightarrow y=0$
$x=1 \rightarrow y=1.5$
$x=2 \rightarrow y=6$
The vertex is $(0,0)$. It is a minimum.
The domain is all real numbers. The range is $y \geq 0$.