\[\boxed{\text{244}\text{\ (244)}\text{.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)}\ y = 3x^{2} - 0,5x + \frac{1}{16} \Longrightarrow\]
\[\Longrightarrow парабола,\ ветви\ \]
\[направлены\ вверх.\]
\[x_{b} = - \frac{b}{2a} = - \frac{- 0,5}{2 \cdot 3} = \frac{0,5}{6} = \frac{1}{12};\]
\[y_{b} = y\left( \frac{1}{12} \right) = 3 \cdot \frac{1}{144} - \frac{1}{2} \cdot \frac{1}{12} +\]
\[+ \frac{1}{16} = \frac{1}{48} - \frac{1}{24} + \frac{1}{16} = \frac{2}{48} =\]
\[= \frac{1}{24} \Longrightarrow\]
\[\Longrightarrow E(y) = \left\lbrack \frac{1}{24}; + \infty \right);\]
\[\textbf{б)}\ y = 2x^{2} + 1,2x + 2 \Longrightarrow\]
\[\Longrightarrow парабола,\ ветви\ \]
\[направлены\ вверх.\]
\[x_{b} = - \frac{b}{2a} = - \frac{1,2}{4} = - 0,3;\]
\[y_{b} = y( - 0,3) =\]
\[= 2 \cdot 0,09 - 1,2 \cdot 0,3 + 2 =\]
\[= 1,82 \Longrightarrow\]
\[\Longrightarrow E(y) = \lbrack 1,82; + \infty);\]
\[\textbf{в)}\ y = - \frac{1}{2}x^{2} + 4x - 5,5 \Longrightarrow\]
\[\Longrightarrow парабола,\ ветви\ \]
\[направлены\ вниз.\]
\[x_{b} = - \frac{b}{2a} = - \frac{4}{2 \cdot \left( - \frac{1}{2} \right)} =\]
\[= - \frac{4}{- 1} = 4;\]
\[y_{b} = y(4) = - \frac{1}{2} \cdot 16 + 4 \cdot 4 -\]
\[- 5,5 = - 8 + 16 - 5,5 = 2,5 \Longrightarrow\]
\[\Longrightarrow E(y) = ( - \infty;2,5\rbrack;\]
\[\textbf{г)}\ y = - 3x^{2} - 2x - 4\frac{2}{3} \Longrightarrow\]
\[\Longrightarrow парабола,\ ветви\ \]
\[направлены\ вниз.\]
\[x_{b} = - \frac{b}{2a} = - \frac{- 2}{2 \cdot ( - 3)} = - \frac{1}{3};\]
\[y_{b} = y\left( - \frac{1}{3} \right) =\]
\[= - 3 \cdot \frac{1}{9} + 2 \cdot \frac{1}{3} - 4\frac{2}{3} = - 4\frac{1}{3} \Longrightarrow\]
\[\Longrightarrow E(y) = \left( - \infty;\ - 4\frac{1}{3} \right\rbrack.\]