Постройте график функции: y=x^2-4|x+1|+5x+4.

Ответ:

\[y = x^{2} - 4|x + 1| + 5x + 4\]

\[\left\{ \begin{matrix} x + 1 \geq 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ y = x^{2} - 4x - 4 + 5x + 4 \\ \end{matrix}\text{\ \ \ \ \ \ \ \ \ } \right.\ \]

\[\left\{ \begin{matrix} x + 1 \leq 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ y = x^{2} + 4x + 4 + 5x + 4 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} x \geq - 1\ \ \ \ \ \ \ \\ y = x^{2} + x \\ \end{matrix}\text{\ \ \ \ \ \ \ \ } \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x \leq - 1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ y = x^{2} + 9x + 8 \\ \end{matrix} \right.\ \]