put function in standard form
f(x)=-4x^2-32x+9
There are many "standard forms". One of which is f(x)=a(x-h)²+k
where (h,k) is the position of the vertex, and a is a constant.
This can be achieved by completing the square of
f(x)=-4x^2-32x+9
=-4(x²+8x-9/4)
=-4(x+4)²+4*4²+9/4
=-4(x+4)²+265/4