Решебник по алгебре 9 класс Мерзляк Задание 972

\[\boxed{\mathbf{972\ (972).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[y = ax^{2} + bx + c;\ \ ( - 1;0);\ \ \]

\[x_{0} = \frac{1}{4};\ \ y_{0} = - \frac{25}{8}\]

\[- \frac{b}{2a} = \frac{1}{4} \Longrightarrow \ a = - 2b\]

\[0 = a - b + c \Longrightarrow \ - 2b - b + c =\]

\[= 0 \Longrightarrow \ \ - 3b + c = 0 \Longrightarrow \ \ c = 3b\]

\[- \frac{25}{8} = a \cdot \frac{1}{16} + b \cdot \frac{1}{4} + c\ \ \ \ \ | \cdot 8\]

\[- 25 = a \cdot \frac{1}{2} + 2b + 8c\ \ \ \ | \cdot 2\]

\[- 50 = a + 4b + 16c\]

\[- 50 = - 2b + 4b + 16 \cdot 3b\]

\[- 2b + 4b + 48b = - 50\]

\[50b = - 50\]

\[b = - 1\]

\[a = - 2 \cdot ( - 1) = 2;\ \ \]

\[c = 3 \cdot ( - 1) = - 3\]

\[Ответ:a = 2;\ \ b = - 1;\ \ c = - 3.\]