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Recently, Noytaptim and Petsche proved that the only totally real parameters$c\in \overline{\mathbb Q}$ for which $f_c(z):=z^2+c$ is postcritically finiteare $0$, $-1$ and $-2$. In this note, we show that the only totally realparameters $c\in \overline{\mathbb Q}$ for which $f_c$ has a parabolic cycleare $\frac14$, $-\frac34$, $-\frac54$ and $-\frac74$.

Totally real points in the Mandelbrot Set