  The growth-rate function for a minor-closed class $\mathcal{M}$ of matroids
is the function $h$ where, for each non-negative integer $r$, $h(r)$ is the
maximum number of elements of a simple matroid in $\mathcal{M}$ with rank at
most $r$. The Growth-Rate Theorem of Geelen, Kabell, Kung, and Whittle shows,
essentially, that the growth-rate function is always either linear, quadratic,
exponential, or infinite. Morover, if the growth-rate function is quadratic,
then $h(r)\ge \binom{r+1}{2}$, with the lower bound coming from the fact that
such classes necessarily contain all graphic matroids. We characterise the
classes that satisfy $h(r) = \binom{r+1}{2}$ for all sufficiently large $r$.
