\[\boxed{\text{220\ (220).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
Пояснение.
Решение.
\[\textbf{а)}\ 2x^{2} - 3x + 7 =\]
\[= 2 \cdot \left( x^{2} - \frac{3}{2}x + \frac{7}{2} \right) =\]
\[= 2 \cdot \left( x^{2} - 2 \cdot \frac{3}{4}x + \frac{9}{16} - \frac{9}{16} + \frac{7}{2} \right) =\]
\[= 2 \cdot \left( \left( x - \frac{3}{4} \right)^{2} - \frac{9}{16} + \frac{56}{16} \right) =\]
\[= 2 \cdot \left( \left( x - \frac{3}{4} \right)^{2} + \frac{47}{16} \right) =\]
\[= 2 \cdot \left( x - \frac{3}{4} \right)^{2} + \frac{47}{8} =\]
\[= 2 \cdot \left( x - \frac{3}{4} \right)^{2} + 5\frac{7}{8}\]
\[\textbf{б)} - 3x^{2} + 4x - 1 =\]
\[= - 3 \cdot \left( x^{2} - 2 \cdot \frac{2}{3}x + \frac{4}{9} - \frac{4}{9} + \frac{1}{3} \right) =\]
\[= - 3 \cdot \left( \left( x - \frac{2}{3} \right)^{2} - \frac{1}{9} \right) =\]
\[= - 3 \cdot \left( x - \frac{2}{3} \right)^{2} + \frac{1}{3}\]
\[\textbf{в)}\ 5x^{2} - 3x =\]
\[= 5 \cdot \left( x^{2}\ - 2 \cdot \frac{3}{10}x + \frac{9}{100} - \frac{9}{100} \right) =\]
\[= 5 \cdot \left( \left( x - \frac{3}{10} \right)^{2} - \frac{9}{100} \right) =\]
\[= 5 \cdot \left( x - \frac{3}{10} \right)^{2} - \frac{9}{20}\]
\[\textbf{г)} - 4x^{2} + 8x =\]
\[= - 4 \cdot \left( x^{2} - 2x + 1 - 1 \right) =\]
\[= - 4 \cdot \left( (x - 1)^{2} - 1 \right) =\]
\[= - 4 \cdot (x - 1)^{2} + 4\]
\[\boxed{\text{220.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]
\[Пересечение\ с\ осью\ Oy:\ \ \]
\[x = 0 \Longrightarrow y = - 6.\]
\[График\ пересекает\ ось\ Oy\ в\ \]
\[точке\ (0;\ - 6).\]
\[Пересечение\ с\ осью\ \text{Ox}:\ \ \ \]
\[y = 0 \Longrightarrow x^{3} - 6x^{2} + 11x - 6 =\]
\[= 0;\]
\[x_{1} = 1 - корень\ уравнения\ \]
\[(методом\ подбора).\]
\[\Longrightarrow x^{3} - 6x^{2} + 11x - 6 =\]
\[= (x - 1)\left( x^{2} - 5x + 6 \right)\]
\[x^{2} - 5x + 6 = 0\]
\[D = 25 - 24 = 1\]
\[x_{2,3} = \frac{5 \pm 1}{2},\ \ x_{2} = 3,\ \ \]
\[x_{3} = 2.\]
\[График\ пересекает\ ось\ \text{Ox}\ в\]
\[\ точках\ (1;0);\ \ (2;0);\ \ (3;0).\]