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

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