Answer
Please see the graph.
Work Step by Step
$g(x) = (x-6)^2+1$
Axis of symmetry:
$g(x) = (x-6)^2+1$
$g(x) = (x- 6)^2+1$
$x=6$
Vertex:
$g(x) = (x-6)^2+1$
$g(6) = (6-6)^2+1$
$g(6)=0^2+1$
$g(6) = 0+1$
$g(6)=1$
The green line $x=6$ is the axis of symmetry, the black dot at $(6,1)$ is the vertex, and the red line is the function $g(x)=(x-6)^2+1$.
