Question

The zeros of a quartic funcations are -2, -1, and 3 (multiplicity of 2). Determine the equation of the function that satisfies this condition and passes through the point (2,24)

Answer 1

Since -2, -1, and 3 (multiplicity of 2) are zeros:
(x+2), (x+1), (x-3)^2 are factors.
f(x) = a * (x+1)(x+2)(x-3)^2
(2,24) is a point on it. Therefore, when x = 2, f(x) = 24
24 = a * (3)(4)(-1)^2.
Solve for a. Put it in f(x).
It is up to you if you want to multiply out all the factors.