Решебник по алгебре 9 класс Мерзляк Задание 379

\[\boxed{\text{379\ (379).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[y = ax^{2} + bx + c;\ \ a \neq 0\]

\[C(4;\ - 10) - вершина;\ \]

\[\ \text{D\ }(1;\ - 1):\]

\[\left\{ \begin{matrix} - \frac{b}{2a} = 4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ ax^{2} + bx + c = - 10 \\ a + b + c = - 1\ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\]

\[\text{\ \ }\left\{ \begin{matrix} b = - 8a\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ ax^{2} - 8ax + c = - 10\ \\ a - 8a + c = - 1\ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} b = - 8a\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ ax^{2} - 8ax + c = - 10\ \\ c = 7a - 1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\text{\ \ \ }\left\{ \begin{matrix} b = - 8a\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ ax^{2} - 8ax + 7a - 1 = - 10 \\ c = 7a - 1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[ax^{2} - 8ax + 7a + 9 = 0\]

\[D = 64a^{2} - 4a(7a + 9) =\]

\[= 64a^{2} - 28a^{2} - 36a =\]

\[= 36a^{2} - 36a = 36\left( a^{2} - a \right) \geq 0\]

\[a^{2} \geq a\]

\[a = 0 - не\ удовлетворяет.\]

\[\left\{ \begin{matrix} a = 1\ \ \ \\ b = - 8 \\ c = 6\ \ \ \\ \end{matrix} \right.\ \]

\[Ответ:a = 1,\ \ \ b = - 8,\ \ \ c = 6.\]