Only $1$ Intersects

$m$ is an integer such that only one of the following three parabolas intersects the $x$ -axis: $\begin{aligned} y &= x^2-2mx+36, \\ y &= x^2-2mx-6m+16, \\ y &= x^2-2(m-1)x+2m^2-16m+49. \end{aligned}$ If $a$ and $b$ are the minimum and maximum values of $m,$ respectively, what is $b-a?$