Let f a :R to R be defined by f a (x)=-x 3 +2x 2 +ax, where a is a real parameter. Prove that the difference equation y(n+1)=f a (y(n)), n=0...

Let fa:R to R be defined by fa(x)=-x3+2x2+ax, where a is a real parameter. Prove that the difference equation y(n+1)=fa(y(n)), n>=0 undergoes a bifurcation at a=1. What kind of bifurcation occurs at this bifurcation point? Explain your answer. 

I have found the equillibrium solutions y1=0, y2=1-1/2 root(4a) and y3=1+1/2 root(4a).

So looking at the derivative of  fa(x), we can see that  y1 is asymptotically stable if a<1 and unstable if a>1..... but I don't really understands what happens for y2 and y3, is it a period doubling? transcritical? And why? Thanks for the help!