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

\[y = kx + l\]

\[A(6;4):\ \ \ 4 = k \cdot 6 + l\]

\[B(4;10):\ \ \ 10 = k \cdot 4 + l\]

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

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

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

\[k = - 3 \Longrightarrow l = 10 - 4 \cdot ( - 3) =\]

\[= 10 + 12 = 22 \Longrightarrow y =\]

\[= - 3x + 22.\]

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

\[A(6;4):\ \ \ \ 4 = 6^{2} + b \cdot 6 + c\]

\[B(4;10):\ \ \ \ 10 = 4^{2} + b \cdot 4 + c\]

\[\left\{ \begin{matrix} 6b + c = - 32\ \ \ \ (1) \\ 4b + c = - 6\ \ \ \ \ \ \ (2) \\ \end{matrix} \right.\ \]

\[(1) - (2):\ \ \ \ \ \ \ 2b = - 26\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ b = - 13\]

\[b = - 13 \Longrightarrow c =\]

\[= - 6 - 4 \cdot ( - 13) = - 6 + 52 =\]

\[= 46 \Longrightarrow y = x^{2} - 13x + 46.\]

\[Ответ:\ \ k = - 3;\ \ l = 22;\ \ \]

\[b = - 13;\ \ c = 46.\]