Determine the equation of the cubic function shown in the gr

Determine the equation of the cubic function shown in the graph below.

Solution

we can see the curve cuts the x axis at x = -4 ; x = 1 , x = 2

Further it cuts y axis at y=10

So, let polynomial be : f(x) = a(x+4)(x-1)(x-2)

find a using (0, 10) : 10 = a(4)(-1)(-2)

a = 10/8 = 5/4

f(x) = (5/4)(x+4)(x-1)(x-2)