\[y = x^{2} + px + q;\ \ (2;5)\]
\[x_{0} = \frac{- p}{2}\text{\ \ }\]
\[- \frac{p}{2} = 2\]
\[p = - 4.\]
\[4 - 4 \cdot 2 + q = 5\]
\[q = 9.\]
\[Ответ:при\ \ p = - 4;\ q = 9.\]