Chapter 8 - Graphing Quadratic Functions - 8.4 - Graphing f(x) = a(x-h)^2 + k - Exercises - Page 446: 21

Vertex: $(4,0)$. Axis of symmetry: $x=4$

The quadratic function in the form $y=a(x-h)^2+k$ has the vertex $(h,k)$ and the axis of symmetry $x=h$. $$f(x)=-\frac18(x-4)^2$$ Rewrite as: $$f(x)=\frac18(x-4)^2+0$$ Therefore $h=4$, $k=0$. The vertex is: $$(h,k)=(4,0).$$ The axis of symmetry is: $$x=4.$$