# Only \(1\) Intersects

**Algebra**Level pending

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