Doug C. answered • 5d

Math Tutor with Reputation to make difficult concepts understandable

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 = ax^{2}+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 = -x^{2}-8x-13

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