Answer:
f(x) = 2(x + 2)(x - 3)(x - 4) or
f(x) = 2x^3 - 10x^2 - 4x + 48
Step-by-step explanation:
If a cubic function has zeros a, b, c, then its equation is
f(x) = k(x - a)(x - b)(x c)
f(x) = k(x - (-2))(x - 3)(x - 4)
f(x) = k(x + 2)(x - 3)(x - 4)
f(5) = k(5 + 2)(5 - 3)(5 - 4)
f(5) = k(7)(2)(1)
f(5) = 14k
We are told f(5) = 28, so we set 14 equal to 28 and solve for k.
14k = 28
k = 2
f(x) = 2(x + 2)(x - 3)(x - 4)
f(x) = 2x^3 - 10x^2 - 4x + 48
