Answer
Please see the graph.
Work Step by Step
$g(x)=x^2+7$
Axis of symmetry:
$g(x)=x^2+7$
$g(x)=(x-0)^2+7$
$x=0$
Vertex:
$g(x)=x^2+7$
$g(0)=0^2+7$
$g(0)=0+7$
$g(0)=7$
The dot at $(0, 7)$ is the vertex, the black line at $x=0$ is the axis of symmetry, and the red line that goes through the dot is the function $g(x)=x^2+7$.
