Algebraically, determine the values of "a" and "b" in the relation y = ax2 + bx - 13 if the vertex is located at (-4, 3).

Answer 1

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

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