Answer
Vertex: $(6,0)$.
Axis of symmetry: $x=6$
Work Step by Step
The quadratic function in the form $y=a(x-h)^2+k$ has the vertex $(h,k)$ and the axis of symmetry $x=h$.
$$f(x)=\frac14(x-6)^2$$ Rewrite as:
$$f(x)=\frac14(x-6)^2+0$$ Therefore $h=6$, $k=0$.
The vertex is: $$(h,k)=(6,0).$$
The axis of symmetry is: $$x=6.$$