При каких значениях a и b парабола y=ax^2+bx+2 проходит через точки M

(3; -1) и K (-6; 26)?

\[y = ax^{2} + bx + 2;\ \ M\ (3; - 1);\ \ \]

\[\text{K\ \ }( - 6;26)\]

\[\left\{ \begin{matrix} 9a + 3b + 2 = - 1\ \ \ | \cdot 2 \\ 36a - 6b + 2 = 26\ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} 18a + 6b = - 6 \\ 36a - 6b = 24 \\ \end{matrix} \right.\ \ ( + )\text{\ \ \ \ }\]

\[\left\{ \begin{matrix} 54a = 18\ \ \ \ \ \ \ \ \ \\ b = \frac{- 6 - 18a}{6} \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} a = \frac{1}{3}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ b = \frac{- 6 - \frac{18}{3}}{6} \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} a = \frac{1}{3}\text{\ \ \ } \\ b = - 2 \\ \end{matrix} \right.\ \]

\[Ответ:\ при\ a = \frac{1}{3};\ \ b = - 2.\ \]