11. On a plane, a parabola divides the plane into two parts, two parabolas can divide the plane into at most seven parts, then how many parts can $n$ parabolas divide the plane into at most?
11. Let $n$ parabolas divide the plane into at most $a_{n}$ parts. To maximize the number of regions divided by $n+1$ parabolas, the $(n+1)$-th parabola should intersect each of the first $n$ parabolas at 4 points. The $(n+1)$-th parabola is divided into $4n+1$ arcs by these $4n$ points, and each arc corresponds to one new region. Therefore, $a_{1}=2, a_{n+1}=a_{n}+(4 n+1)$. Thus, $a_{n}=$ $\left(a_{n}-a_{n-1}\right)+\left(a_{n-1}-a_{n-2}\left(+\cdots+\left(a_{2}-a_{1}\right)+a_{1}=2 n^{2}-n+1\right.\right.$, which means $n$ parabolas can divide the plane into at most $2 n^{2}-n+1$ parts.