\(a\ne0\)
\(\left\{{}\begin{matrix}-\frac{b}{2a}=2\\4ac-b^2=0\\9a+3b+c=4\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}b=-4a\\4ac-16a^2=0\\9a-12a+c=4\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}b=-4a\\c-4a=0\\-3a+c=4\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}a=4\\b=-16\\c=16\end{matrix}\right.\)