\[\boxed{\mathbf{209}\text{.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]
\[y = x^{2} + px + q\]
\[\textbf{а)}\ по\ теореме\ Виета:\]
\[\ \left\{ \begin{matrix} x_{1} \cdot x_{2} = q = 12\ \ \ \ \ \ \ \\ x_{1} + x_{2} = - p = - 7 \\ \end{matrix} \right.\ ;\]
\[\textbf{б)}\ (0;6):\ \ \ q = 6;\]
\[(2;0):\ \ \ \ 0 = 4 + 2p + q;\]
\[\left\{ \begin{matrix} q = 6\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 4 + 2p + 6 = 0 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} q = 6\ \ \ \ \ \ \ \ \\ 2p = - 10 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} q = 6\ \ \\ p = - 5 \\ \end{matrix} \right.\ ;\]
\[\textbf{в)}\ координаты\ вершины:\ \ \]
\[(6;24).\]
\[\left\{ \begin{matrix} 6 = - \frac{p}{2}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ 24 = 36 + 6p + q \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} p = - 12\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 24 = 36 - 6 \cdot 12 + q \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} p = - 12 \\ q = 60\ \ \\ \end{matrix} \right.\ .\]