  The best uniform polynomial approximation of the checkmark function
$f(x)=|x-\alpha |$ is considered, as $\alpha$ varies in $(-1,1)$. For each
fixed degree $n$, the minimax error $E_n (\alpha)$ is shown to be piecewise
analytic in $\alpha$. In addition, $E_n(\alpha)$ is shown to feature $n-1$
piecewise linear decreasing/increasing sections, called V-shapes. The points of
the alternation set are proven to be monotone increasing in $\alpha$ and their
dynamics are completely characterized. We also prove a conjecture of Shekhtman
that for odd $n$, $E_n(\alpha)$ has a local maximum at $\alpha=0$.
