Prove that the inner product associated with a positive definite quadratic form $q(x)$ is given by the polarization formula $\langle x, y\rangle = \frac{1}{2}[q(x+y) - q(x) - q(y)]$.
How will I be able to do this problem. I know in order to be a positive definite you need the following axioms to be verified: bilinearity, positivity and symmetric. Thus we need that $\langle x, y\rangle = x^TKy$ for $x,y \in R^n$ but how do I go on to apply that here?