Maximizing a Quadratic Form

Let $A$ be an $n \times n$ square matrix and $x \in \mathbb{R}^n$. You want to find the maximum of the quadratic form $x^\top A x$. 1. Assume $A$ is symmetric and $\|x\|_2 = 1$. What is the maximum value of $x^\top A x$, and where is it achieved? 2. What if $A$ is not symmetric? Show how to reduce this case to the symmetric one. 3. What happens if you drop the unit-norm constraint and optimize over all $x \in \mathbb{R}^n$?