\[\boxed{\text{239\ (239).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[y = x^{2} + \text{bx} + c;\ \ \ \]
\[вершина\ (6;\ - 12).\]
\[x_{b} = - \frac{b}{2a} = - \frac{b}{2 \cdot 1} = - \frac{b}{2};\]
\[y_{b} = \left( - \frac{b}{2} \right)^{2} + b \cdot \left( - \frac{b}{2} \right) + c =\]
\[= \frac{b^{2}}{4} - \frac{b^{2}}{2} + c = c - \frac{b^{2}}{4};\]
\[Так\ как\ вершина\ имеет\ \]
\[координаты\ (6;\ - 12),\ \]
\[подставим:\]
\[\left\{ \begin{matrix} - \frac{b}{2} = 6\ \ \ \ \ \ \ \ \ \ \ \\ c^{\backslash 4} - \frac{b^{2}}{4} = - 12 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} b = - 12\ \ \ \ \ \ \ \ \ \ \ \ \\ 4c - b^{2} = - 48 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} b = - 12\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 4c - ( - 12)^{2} = - 48 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} b = - 12 \\ 4c = 96\ \\ \end{matrix} \Longrightarrow \right.\ \left\{ \begin{matrix} b = - 12 \\ c = 24\ \ \ \\ \end{matrix} \right.\ \]
\[Ответ:при\ b = - 12;\ \ c = 24.\]