Is there a named theorem for the fact that two points define a line, and three points define a quadratic function?

Question

In particular, is there a theorem stating the fact that a polynomial function of degree d is defined by d+1 points?

I'm asking because I want to use this fact in a different proof but I want to be able to cite a theorem for it if one exists.

Answer 1

This is known as the unisolvence theorem.