Find the standard form given three points of a parabola

Question

Find the standard form given three points of a parabola.

(-6,0)

(-4,0)

(-3,-18)

(I tried to use a system of equations, but I don't know how to solve it. This is what I did;

f(x) = a(x - h)² + k

0 = a(-6 - h)² + k

0 = a(-4 - h)² + k

-18 = a(-3 - h)² + k)

Answer 1

The first 2 points tell you that the roots of the polynomial which defines polynomial for the parabola are -6 and -4.

That means the equation is A(x+6)(x+4).

The A is determined by the 3rd point as -18 = A(-3+6)(-3+4) which makes A = -6

....and there you have it!