The function $f$ is defined by $f(x)=a{x}^2+bx+c$, where $a$, $b$, and $c$ are constants. The graph of $y=f(x)$ has a vertex at $(2,-3)$. If the function $g$ is defined by $g(x)=f(x)+7$, what is the minimum value of $g(x)$?