Solving for a Cubic Function with Given Points

[brycenrg]

Homework Statement

Find an expression for a cubic function f if f(1)=6 and f(-1)=f(0)=f(2)=0

Homework Equations

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

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 ?

 

[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".

 

[LCKurtz]

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