2. For the quadratic function $y=x^{2}-4 a x+5 a^{2}$ $-3 a$ in terms of the independent variable $x$, the minimum value $m$ is a function of $a$, and $a$ satisfies the inequality $0 \leqslant$ $a^{2}-4 a-2 \leqslant 10$. Then the maximum value of $m$ is $\qquad$ $ـ$
2. 18 .

Solving $0 \leqslant a^{2}-4 a-2 \leqslant 10$ yields $-2 \leqslant a \leqslant 2-\sqrt{6}$ or $2+\sqrt{6} \leqslant a \leqslant 6$. Also, $m=a^{2}-3 a$, considering the quadratic function, $m=a^{2}-3 a$ when $-2 \leqslant a \leqslant 2-\sqrt{6}$ and $2+\sqrt{6} \leqslant a \leqslant 6$, we can see that the maximum value occurs when $a=6$, thus $m=6^{2}-3 \times 6=18$