The function $f$ is defined by $f(x)=a{x}^2+bx+c$, where $a,b,c$ are constants. The graph of $y=g(x)$ is the result of translating the graph of $y=f(x)$ up $k$ units, where $k>0$. If the $y$-intercept of the graph of $y=f(x)$ is $P$, what is the $y$-intercept of the graph of $y=g(x)$ in terms of $P$ and $k$?