Question

Find an expression for a cubic function f if f(1)=24 and f(-3)=f(0)=f(2)=0

Answer 1

Refer to the Mathematica 9 plot and solution attached.

Answer 2

You can do this without Mathematica...unless your question required software.
A cubic function can be generally expressed as \(\large f(x) =ax^3+bx^2+cx+d\)
With the values you have, you can essentially create a system of 4 equations and 4 unknowns:

\[\large f(1)=a(1)^3+b(1)^2+c(1)+d=24\\
\large f(-3)=a(-3)^3+b(-3)^2+c(-3)+d=0 \\
\large f(0)=a(0)^3+b(0)^2+c(0)+d=0 \\
\large f(2)=a(2)^3+b(2)^2+c(2)+d=0 \]
Notice how the 3rd question though immediately tells you that \(d=0\), effectively giving you now a system of 3 equations to solve for a, b, c

Answer 3

3rd equation*