Determine the equation, f(x), of a cubic function for which:

Question

Determine the equation, f(x), of a cubic function for which:

f(-1)=0

f(2)=0

f(3)=0

and

f(0)=4

Answer 1

-1,2 and 3 are the x intercepts

f(x) = a(x+1)(x-2)(x-3)

f(0)=4 = a(1)(-2)(-3) = 6a

a = 4/6 = 2/3

f(x) = (2/3)(x+1)(x-2)(x-3)

or

f(x) = (2/3)(x^2-x-2)(x-3)

= (2/3)(x^3 -4x^2 +x+6)

= (2x^3)/3 -(8x^2)/3 + 2x/3 +4

Answer 2

If f(x) is polynomial,

the first three conditions mean f(x)=a(x+1)(x-2)(x-3)=a(x³-4x²+x+6)

to have f(0)=4 a=4/6

f(x)=(4/6)x³-(8/3)x²+(4/6)x+4

Answer 3