hi I need some help understanding the hint this exercise gives:

Where$\displaystyle I=[-2,2]$ and

$\displaystyle A_1=\{x \in I : Q_c(x)\in I \}$.

$\displaystyle p_+$ is the fixed point of $\displaystyle Q_c $ in $\displaystyle [0,2]$.

$\displaystyle p_+=\frac{1+ \sqrt{1-4c}}{2}$

I dont understand why it suffices to find the c-values the hint points to guarantee the conclusion for $\displaystyle x \in [0,\frac{1}{2}]$

thank you!