Let $f(x)=a+bx^2$. Define $f_n(x)$ to be the $n$-fold composition of $f$. That is $f_1(x)=f(x)$ $f_2(x)=f \circ f(x)$ $f_n(x)=f \circ f_{n-1}(x), n \ge 2$
Is there a way to find a formula for $f_n$?
I tried to write down $f_2$, $f_3,\ldots$, but I don't see any pattern.