Can you use the same methods used for finding quadratic equations given three points to find any degree of function? Using the equation:

$\displaystyle y=ax^{n_1}+bx^{n_1-1}+cx^{n_1-2}\cdots +dx^0$

Needing $\displaystyle n+1 $ number of points per degree to solve?

I attempted to ask my algebra teacher but she looked dumb founded...so I just left.