For a homework problem we are asked to work with the equation
$$ \phi (x) = \frac{1}{2}x^T Ax - x^T b $$
and prove something about its minimum given a symmetric positive definite matrix. We worked through a proof in class but there are a few parts I am unsure of and I am trying to research them. Though, I am not sure how to search on it because I am not sure of the name of this equation.
I know that it is related to the Arnoldi iteration and GMRES but searching on those doesn't turn up much, if anything, related to this function.
What is the name of this function? Where does it come from?