Critical points of a nonnegative quadratic form on a subspace

Let $Q(x)=x^tAx$ for some square symmetric matrix $Ain R^{ntimes n}$, such that $Q(x)geq0$ for each $xin R^n$. Let $S$ be an affine subspace of $R^n$. How can I show that if $y$ is a critical point of $Q$ on $S$, then $y$ is a point of global minimum of $Q$ on $S$?