Question

Determine the cubic function with zeros -2, 3 and 4 and f(5) = 28

Answer 1

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