# Cubic function

1. Aug 26, 2013

### brycenrg

1. The problem statement, all variables and given/known data
Find an expression for a cubic function f if f(1)=6 and f(-1)=f(0)=f(2)=0

2. Relevant equations
I figured it out but im not sure why we use the equation f(x) = a[x-(-1)](x-0)(x-2)

3. The attempt at a solution
Im assuming its because if u times that equation that is a cubic function, but does it have anything todo with f(-1)=f(0)=f(2)=0 ?

2. Aug 26, 2013

### symbolipoint

Certainly yes. Those f(c)=0 values mean that some binomial, x-c, is a factor of the function's expression or its definition. Your exercise gives you three of them and they are for a cubic function. The binomial factors will take care of your roots for your function. The coefficient, "a", is for accounting for the remainder in case you choose a value for x which is not a root. The given f(1)=6 helps you to find "a".

3. Aug 26, 2013

### LCKurtz

@brycenbrg: Look up the factor theorem in your text or online.