Let $f_c : z \rightarrow z^2 +c$ and $Q_a: x \rightarrow ax(1-x)$, I have to show that for $c \in [-2, \frac{1}{4}]$ there is an $a\in[1,4]$ such that $f_c$ is conjugate to $Q_a$
Unfortunately, I'm uncertain about how to proceed. My initial thought was to explore periodic or fixed points, given their preservation under conjugacy, but implementing this approach has proven challenging.
Is there a simpler method that can help identify such homeomorphisms more effectively?