I have the following sequence: $(x_{n})_{n\geq 0}$, $x_{0}=a$, $x_{n+1}=x^{2}_{n}-4x_{n}+6$

I need to find all $a$ values such that $(x_{n})_{n\geq 0}$ to be convergent.

I took $f(x)=x^{2}-4x+6$ and I found 2 fixed points, $2$ and $3$ , solutions of $f(x)=x$.I know that if $(x_{n})_{n\geq 0}$ is convergent then it converges to one of the points I found.I don't know how to continue.How to approach an exercise like this?