A quadratic form associated with a symmetric matrix $A$ is the scalar $x^T A x$ for vectors $x$. Quadratic forms are fundamental in optimization and geometry. For $A = \begin{pmatrix} 2 & 1 \\ 1 & 3 \end{pmatrix}$ and $x = \begin{pmatrix} 1 \\ 2 \end{pmatrix}$, compute the quadratic form $x^T A x$.