The function $f(x)$ is a quadratic function defined by $f(x)=a(x-h{)}^2+k$, where $a>0$. The function $g(x)$ is defined by $g(x)=f(x+c)$. If the minimum of $f(x)$ occurs at $x=7$ and the minimum of $g(x)$ occurs at $x=2$, what is the value of $c$?