\[\begin{array}{l}
Dinh\,\,I\left( {2; - 2} \right)\\
\Rightarrow \frac{{ - b}}{{2a}} = 2 \Leftrightarrow b = - 4a.\\
I \in \left( P \right)\\
\Rightarrow - 2 = 4a + 2b + 2\\
\Leftrightarrow - 4 = 4a - 8a\\
\Leftrightarrow - 4a = - 4\\
\Leftrightarrow a = 1\\
\Rightarrow b = - 4.\\
\Rightarrow \left( P \right):\,\,\,y = {x^2} - 4x + 2.
\end{array}\]