First, f(x) can be written as a y, so y=x2-6x-16
Next, you can have two options here: 1) change this equation into the vertex form of a parabola or 2) find the coordinate for the vertex.
1) The first option is more detailed - The vertex form of a parabola is: y=(x-h)2+k where the (h,k) is the vertex of the parabola.
We will have to use “completing the square” method to transform the equation from the general form to the vertex form.
y+16+9 = x2-6x+9
y+25 = (x-3)2
y=(x-3)2-25, so the vertex is (3, -25)
2) The second option uses the coordinate (-b/2a, f(-b/2a)), where ax2+bx+c is your equation in standard form.
So, a=1 and b=-6 therefore, (3, f(3)) yields a vertex at (3, -25)