\[\boxed{\text{243}\text{\ (243)}\text{.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)}\ y = x^{2} + 2x - 15\]
\[x_{b} = - \frac{b}{2a} = - \frac{2}{2} = - 1;\]
\[y_{b} = ( - 1)^{2} - 2 \cdot 1 - 15 = - 16;\]
\[x^{2} + 2x - 15 = 0\]
\[D_{1} = 1 + 15 = 16\]
\[x_{1} = - 1 - 4 = - 5;\ \ x_{2} =\]
\[= - 1 + 4 = 3\]
\[E(y) = \ \lbrack - 16;\ + \infty).\]
\[При\ x \in ( - \infty; - 1)\ функция\ \]
\[убывает\ и\ при\ \]
\[x \in ( - 1; + \infty)\ возрастает.\]
\[y < 0\ \ при\ x \in ( - 5;3)\ и\ y > 0\ \ \]
\[при\ \ x \in ( - \infty; - 5) \cup (3; + \infty).\]
\[\textbf{б)}\ y = 0,5x^{2} - 3x + 4\]
\[x_{b} = - \frac{b}{2a} = - \frac{- 3}{- 2 \cdot 0,5} = 3;\]
\[y_{b} = 0,5 \cdot 3^{2} - 3 \cdot 3 + 4 = - 0,5.\]
\[0,5x^{2} - 3x + 4 = 0\]
\[D = 9 - 0,5 \cdot 16 = 1\]
\[x_{1} = \frac{3 + 1}{1} = 4;x_{2} = \frac{3 - 1}{1} = 2.\]
\[E(y) = \lbrack - 0,5;\ + \infty).\]
\[При\ x \in ( - \infty;3)\ функция\ \]
\[убывает\ и\ при\ \]
\[x \in (3; + \infty)\ возрастает.\]
\[y < 0\ \ при\ x \in (2;4)\ и\ y > 0\ \ \]
\[при\ \ x \in ( - \infty;2) \cup (4; + \infty).\]
\(в)\ y = 4 - 0,5x^{2}\)
\[4 - 0,5x^{2} = 0\]
\[0,5x^{2} = 4\]
\[x^{2} = 8\]
\[x \approx \pm 2,8.\]
\[x_{b} = \frac{0}{1} = 0;\]
\[y_{b} = 4.\]
\[E(y) = ( - \infty;4\rbrack;\]
\[D(y) = R.\]
\[Функция\ возрастает\ при\ \]
\[x \in ( - \infty;0);\]
\(убывает\ при\ x \in (0; + \infty).\)
\[y > 0\ при\ - 2,8 < x < 2,8;\]
\[y < 0\ \ при\ x < - 2,8;\ \ x > 2,8.\]
\[\textbf{г)}\ y = 6x - 2x^{2}\]
\[x_{b} = - \frac{b}{2a} = - \frac{6}{- 4} = \frac{3}{2};\]
\[y_{b} = 6 \cdot \frac{3}{2} - 2 \cdot \frac{9}{4} = 4,5;\]
\[6x - 2x^{2} = 0\]
\[2x(3 - x) = 0\]
\[x_{1} = 0\ \ и\ \ \ x_{2} = 3;\]
\[E(y) = ( - \infty;4,5\rbrack\]
\[y > 0\ \ при\ \ x \in (0;\ 3)\ и\ \ \]
\[y < 0\ \ \ при\ \ \]
\[x \in ( - \infty;0) \cup (3; + \infty);\]
\[Функция\ возрастает\ \]
\[при\ x \in ( - \infty;1,5)\ \ и\ \]
\[убывает\ \ (1,5; + \infty).\]
\[\textbf{д)}\ y = (2x - 7)(x + 1)\]
\[y = 2x^{2} - 5x - 7\]
\[x_{b} = - \frac{- 5}{4} = \frac{5}{4} = 1,25;\]
\[y_{b} = 2 \cdot \frac{25}{4} - 5 \cdot \frac{5}{4} - 7 =\]
\[= - 10,125;\]
\[x_{1} = - 1\ \ \ и\ \ \ x_{2} = 3,5 \Longrightarrow\]
\[\Longrightarrow нули\ функции;\]
\[E(y) = \lbrack - 10,125;\ + \infty).\]
\[При\ x \in ( - \infty;1,25)\ функция\ \]
\[убывает\ и\ при\ \]
\[x \in (1,25; + \infty)\ возрастает.\]
\[y < 0\ \ при\ x \in ( - 1;3,5)\ и\ \]
\[y > 0\ \ при\ \ \]
\[x \in ( - \infty; - 1) \cup (3,5; + \infty).\]
\[\textbf{е)}\ y = (2 - x)(x + 6)\]
\[y = - x^{2} - 4x + 12\]
\[x_{b} = - \frac{- 4}{- 2} = - 2;\ \ y_{b} = 16;\]
\[x_{1} = 2\ \ и\ \ x_{2} = - 2 \Longrightarrow\]
\[\Longrightarrow нули\ функции;\]
\[E(y) = ( - \infty;16\rbrack\]
\[y > 0\ \ при\ \ x \in ( - 6;\ - 2)\ и\ \ \]
\[y < 0\ \ \ при\ \ \]
\[x \in ( - \infty; - 6) \cup (2; + \infty);\]
\[Функция\ возрастает\ \]
\[при\ x \in ( - \infty; - 2)\ \ и\ \]
\[убывает\ \ ( - 2; + \infty).\]