Question

номер 2. Алгебра ...

Answer 1

$y = 2 {x}^{2} - 9x + 4$
а) Xв = -b/2a = - -9/2*2 = 9/4
Yв = 2*(9/4)^2 - 9*9/4 + 4 = 2*81/16 - 81/4 + 4 = 81/8 - 81/4 + 4 = -81/8 + 4 = -81/8 + 32/8 = -49
(9/4; -49) -- вершина параболы

б) x = 9/4

в) a = 2 > 0 => ветви параболы направлены вверх

г) y = 0,
$2 {x}^{2} - 9x + 4 = 0 \\ d = {b}^{2} - 4ac = 81 - 4 \times 2 \times 4 = 49 \\ x1 = \frac{9 + 7}{2 \times2 } = \frac{16}{4} = 4 \\ x2 = \frac{9 - 7}{2 \times 2} = \frac{2}{4} = \frac{1}{2}$
(4; 0), (1/2; 0).

д) x = 0
$y = 2 \times 0 - 9 \times 0 + 4 = 4$
(0; 4).