Solution
= Solution
For every <tangent vector> $v\perp x_0$, stationarity of $Q$ on the sphere gives $2v^TAx_0=0$. Hence $Ax_0$ is parallel to $x_0$, say $Ax_0=Ex_0$. Taking the <inner product> with $x_0$ gives $E=Q(x_0)$. The spectral theorem shows that this is the largest <eigenvalue>.
For $A=\begin{pmatrix}1&t\\t&1\end{pmatrix}$ the <eigenvalues> are $1\pm t$, so
$$
E(t)=1+|t|.
$$
Its graph is a V translated upward and is convex.