The axis of symmetry for a parabola opening up or down is given by x = -b/2a. Since the x-coordinate of the vertex lies on the axis of symmetry it is true that -b/2a = -4, which results in b = 8a.
Also since y = ax2+bx -13, and the vertex is at (-4,3), that means when x = -4, y = 3.
After substituting all that we know:
3 = a(16) + (8a) (-4) -13
This results in a = -1. Since b = 8a, b = -8.
So, final equation is y = -x2-8x-13