Every convex form of functions is convex?

Question

The function $f(x,y)=a(x-b)^2+c(y-d)^2$ is convex. It is well known and I can prove it ($a>0, b>0$).

What if $F(x,y)=a(g(x,y)-b)^2+c(h(x,y)-d)^2$?

1. Is $F$ always a convex function?

Or

2. if $g$ and $h$ is convex, then is $F$ always a convex function?