Find A and B given the vertex (2,-4)

Question

In this question, A and B means the A and B variables in the equation Y=Ax^2+Bx+c

Answer 1

Let's rephrase the question: Given the vertex of parabola is (2, -4), find A and B in the quadratic function

y = Ax² + Bx + c

x-coordinate (2) of the vertex is

b B

x = - ----, => x_v = - ---- = 2, then B = -4A

2a 2A

y = f(x), so y-coordinate (-4) of the vertex is found by plugging in x-coordinate in the equation

y_v = Ax_v² + Bx_v + c = A*2² + (-4A)*2 + c = -4, then

4A - 8A + c = -4, 4A = c + 4

A = (c + 4) / 4

B = -4A = -4(c + 4) / 4 = -c - 4

Answer: In the quadratic function y = Ax² + Bx + c, where c is a constant, with the given vertex (2, -4),

A = (c + 4) / 4 and B = -c - 4

Answer 2

I need a number here somewhere, otherwise I can just give you the general answer.