Answer
Please see the graph.
Work Step by Step
$H(x)=1/2*(x-6)^2-3 $
Axis of symmetry:
$H(x)=1/2*(x-6)^2-3$
$H(x)=1/2*(x−6)^2-3$
$x=6$
Vertex:
$H(x)=1/2*(x-6)^2-3$
$H(6)=1/2*(6-6)^2-3$
$H(6)=1/2*(0)^2-3$
$H(6)=0-3$
$H(6)=-3$
The red line is the function $f(x)=1/2*(x-6)^2-3$, the line at $x=6$ is the axis of symmetry, and the point $(6,-3)$ is the vertex.
