The function $g(x)=p{x}^2+qx+r$, where $p$ and $r$ are constants, is a quadratic function whose graph in the $xy$-plane is a parabola that opens downward and has a vertex at $(h,k)$. If $k>0$and $g(-1)=g(7)$, which of the following must be true?
I. $q<0$
II. $r>k$