a)
[tex]ZW (-∞; \frac{9}{2} > [/tex]
c)
[tex]f(x) = - 2 {x}^{2} + 6x \\ a = - 2 \: \: \: b = 6 \\ x = - \frac{6}{2 \times( - 2)} = \frac{6}{4} = 1 \frac{2}{4} = 1.5[/tex]
D)
[tex]f(x) = a(x - p {)}^{2} + q[/tex]
[tex]∆ = {6}^{2} - 4 \times ( - 2) \times 0 = 36[/tex]
[tex]p = - \frac{6}{2 \times ( - 2)} = \frac{6}{4} = 1.5 \\ q = - \frac{36}{4 \times ( - 2)} = \frac{36}{8} = 4 \frac{3}{8} [/tex]
[tex]f(x) = - 2(x - 1.5 {)}^{2} + 4 \frac{3}{8} [/tex]
e)
[tex]f(x) = a(x - x1)(x - x2)[/tex]
[tex] \sqrt{∆} = 6[/tex]
[tex]x1 = \frac{ - b - \sqrt{∆} }{2a} = \frac{ - 6 - 6}{2 \times ( - 2)} = \frac{ - 12}{ - 4} = 3 \\ x2 = \frac{ - b + \sqrt{∆} }{2a} = \frac{ - 6 + 6}{2 \times ( - 2)} = 0[/tex]
[tex]f(x) = - 2(x - 3)(x - 0)[/tex]
