При каких значениях b, c, k и I графики функций y=kx+I и y=x^2+bx+c пересекаются в точках A(-4;4) и B(-6;10)?

\[y = kx + l\]

\[A( - 4;4):\ \ \ 4 = k \cdot ( - 4) + l\]

\[B( - 6;10):\ \ \ 10 = k \cdot ( - 6) + l\]

\[\left\{ \begin{matrix} - 4k + l = 4\ \ \ \ \ (1) \\ - 6k + l = 10\ \ \ (2) \\ \end{matrix} \right.\ \]

\[(2) - (1):\ - 2k = 6\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ k = - 3\]

\[k = - 3 \Longrightarrow l = 4 + 4 \cdot ( - 3) =\]

\[= 4 - 12 = - 8.\]

\[y = x^{2} + bx + c\]

\[A( - 4;4):\ \ \ 4 =\]

\[= ( - 4)^{2} + b \cdot ( - 4) + c\]

\[B( - 6;10):\ \ \ 10 =\]

\[= ( - 6)^{2} + b \cdot ( - 6) + c\]

\[\left\{ \begin{matrix} - 4b + c = - 12\ \ \ (1) \\ - 6b + c = - 26\ \ \ (2) \\ \end{matrix} \right.\ \]

\[(1) + (2):\ \ 2b = 14\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ b = 7\]

\[b = 7 \Longrightarrow c = - 12 + 4 \cdot 7 =\]

\[= - 12 + 28 = 16.\]

\[Ответ:\ \ k = - 3;\ \ l = - 8;\ \]

\[\ b = 7;\ \ c = 16.\]