  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 finite
are $0$, $-1$ and $-2$. In this note, we show that the only totally real
parameters $c\in \overline{\mathbb Q}$ for which $f_c$ has a parabolic cycle
are $\frac14$, $-\frac34$, $-\frac54$ and $-\frac74$.
