Question

stie cineva va rog!!​

Answer 1

Răspuns:

Explicație pas cu pas:

$V(\frac{-b}{2a}, \frac{-\Delta}{4a})\\\\\implies \frac{-b}{2a} = 4 \implies -b = 8a \implies b = -8a\\\\\implies \frac{-\Delta}{4a} = 2\implies -\Delta = 8a\implies \Delta = -8a = b\\\\b^2 - 4ac = b\implies b^2 - b = 4ac\implies b(b-1) = 4ac\\\\2 = \textrm{Solutie a ecuatiei y = 0}\Rightarrow 2 = \frac{-b}{2a} \pm \frac{\sqrt{\Delta}}{2a} = 4 \pm \frac{\sqrt{-8a}}{2a}\\\\\implies \frac{\cancel{2}\sqrt{-2a}}{\cancel{2}a} = 2\\\\ \sqrt{-2a} = 2a\\\\ -2a = 4a^2\\\\ -2 = 4a\\\\a = \frac{-2}{4} = \frac{-1}{2}\implies b = -8a = -8\cdot\frac{-1}{2} = 4\\\\ b^2 - b = 4ac \implies c = \frac{b(b-1)}{4a} = \frac{4\cdot 3}{4\cdot \frac{-1}{2}} = -6\\\\\implies abc = \frac{-1}{2}\cdot 4\cdot -6 = 12$

$G_f \cap Ox = \{(\sqrt{3}, 0)\}\implies \sqrt{3} = \frac{-b}{a}\\\\B\in G_f \implies f(2\sqrt{3}) = 2 \implies a\cdot 2\sqrt{3} + b = 2\\ b = 2 - a\cdot 2\sqrt{3} = 2(1 - a\sqrt{3})\\\\\sqrt{3} = \frac{-b}{a}\implies \frac{-2(1-a\sqrt{3})}{a} = \sqrt{3}\implies a\sqrt{3} = -2+2a\sqrt{3}\implies a\sqrt{3} = 2\implies a = \frac{2}{\sqrt{3}} = \frac{2\sqrt{3}}{3}\\\\\implies b = 2 - \frac{2}{\sqrt{3}}\cdot 2\sqrt{3} = 2-4 = -2\\\\f(x) = \frac{2\sqrt{3}}{3}x - 2$