Chapter 8 - Graphing Quadratic Functions - 8.4 - Graphing f(x) = a(x-h)^2 + k - Exercises - Page 447: 33

Vertex: $(-3,1)$. Axis of symmetry: $x=-3$

The quadratic function in the form $y=a(x-h)^2+k$ has the vertex $(h,k)$ and the axis of symmetry $x=h$. Given: $$f(x)=-4(x+3)^2+1.$$ Rewrite as: $$y=-4(x-(-3)^2+1.$$ Therefore $h=-3$, $k=1$. The vertex is: $$(h,k)=(-3,1).$$ The axis of symmetry is: $$x=-3.$$