Answer
Please see the graph.
Work Step by Step
$g(x)=-3x^2$
Axis of symmetry:
$g(x)=-3x^2$
$g(x)=-3(x-0)^2$
$x=0$
Vertex:
$g(x)=-3x^2$
$g(0)=-3*(0^2)$
$g(0)=-3*0$
$g(0)=0$
The red line is the function $g(x)=-3x^2$, the orange line of $x=0$ is the axis of symmetry, and the point $(0,0)$ is the vertex of the function.
