This is an excerpt from my math models textbook. It's about Lagrange Polynomials which is a technique that lets you fit a polynomial to a set of any number of unique points (x_1,y_1) ... (x_n,y_n) so long as all your x-values are different (otherwise it wouldn't be a function, and couldn't be a polynomial). The polynomial you'll calculate will be the unique, lowest degree polynomial that passes through all points.
If you're not very convincing, convince yourself that the polynomial is not cubic. When you fail, you will be convinced that it is cubic. QED