Calculus 3: Gradient Vector help?

so I had a test today, and the equation was f(x,y) = -x^2- y^2 at the point (2,3,-13). The question was what is the fastest uphill direction it should go. What I did was I found the Gradient of f and multiplied it by a negative. Is what I did correct? Because the graph is a parabolic bowl that opens downward, and because the graph is opening downwards, the gradient vector should point down also right?