I'm trying to prove that the real slice of a Mandelbrot set is M n R =[-2,1/4]

I've tried researching it on the internet but everything I find seems to just state this and not prove it.

The hint I've been given to start is is to let

$\displaystyle c$\in$$(1/4, $\displaystyle $\infty$$) proving that for each $\displaystyle $z$$\in$R$ that $\displaystyle f$_{\text{c}}$(z)-z $\geq$ c -$1/4

where $\displaystyle f$_{\text{c}}$(z)= z^2+c$

Any help would be greatly appreciated