The function $f$ is defined by $f(x)=(x-p{)}^2+q$, where $p$ and $q$ are integer constants. The functions $g$ and $h$ are equivalent to function $f$, where $k$ and $m$ are constants. Which of the following equations displays the $y$-coordinate of the $y$-intercept of the graph of $y=f(x)$ in the $xy$-plane as a constant or coefficient?

I. $g(x)=x^2-2px+k$
II. $h(x)=(x-p{)}^2+m$