Last week we introduced the simple two-dimensional function
$$ f(x_1,x_2)=x_1^2+x_1x_2+10x_2^2-5x_1-3x_2, $$which is of the form (in terms of vectors and matrices)
$$ f(\boldsymbol{x})=\frac{1}{2}\boldsymbol{x}^T\boldsymbol{A}\boldsymbol{x}-\boldsymbol{b}^T\boldsymbol{x}, $$where we have
$$ \boldsymbol{x}=\begin{bmatrix} x_1 \\ x_2\end{bmatrix}, $$ $$ \boldsymbol{b}=\begin{bmatrix} 5 \\ 3\end{bmatrix}, $$and
$$ \boldsymbol{A}=\begin{bmatrix} 2 & 1\\ 1& 20\end{bmatrix}. $$