Lời giải:
Ta có \(\left\{\begin{matrix} g(-2)=9\\ g(-1)=2\\ g(1)=6\end{matrix}\right.\Leftrightarrow \left\{\begin{matrix} 4a-2b+c=9(1)\\ a-b+c=2(2)\\ a+b+c=6(3)\end{matrix}\right.\)
Lấy \((3)-(2)\Rightarrow 2b=4\Rightarrow b=2\)
\((3)+(2)\Rightarrow 2(a+c)=8\Rightarrow a+c=4(4)\)
\((1)\Leftrightarrow 4a+c=9+2b=9+2.2=13(5)\)
Lấy \((5)-(4)\Rightarrow 3a=13-4=9\Rightarrow a=3\)
\(c=4-a=4-3=1\)
Vậy $a=3; b=2; c=1$