SOLUTION: come up with a polynomial function that goes through these four points: (0, 0) (1, 2) (3, -2) (5, 5) Thank you.

We have 4 points, and a cubic (3rd degree) polynomial has 4 
coefficients, so we will assume a cubic polynomial function:



We substitute each point:






That simplifies to this system of equations:



Since D=0 the system reduces to



We can divide the last equation by 5, so it simplifies further to:



Solve that system and get , , ,
and we already had .

So



becomes 

Edwin