Find the critical points by taking the derivative of this equation, y'=2x+8. Set this equal to 0, since the minimum is the point where the slope at that point is 0. (Remember that the physical meaning of the derivative at a point is the slope of the equation at that point.) Solve for all possible values of x where y'=2x+8=0. Subtracting 8 from both sides and then dividing 2 on each side, we get x=-4.
Plug this back into the initial equation to get f(x)=(-4)2+8(-4)-4. This yields (-4, -20).