$x \cdot x$ in inner product space is a quadratic form

Question

Given an inner product space with some inner product $\cdot$ , how can I prove that $x \cdot x$ for any vector $x= (x_1,... x_n)$ is a quadratic form in $x_i$?

I know how to recover an inner product given a quadratic form but am not sure how to show this is a quadratic form. Any help is appreciated.