[tex]f(x) = 3x^{2}+4x-2\\\\f(x) = 0\\\\3x^{2}+4x-2 = 0\\\\a = 3, \ \ b = 4, \ \ c = -2\\\\M. \ zerowe:\\\\\Delta = b^{2}-4ac = 4^{2}-4\cdot3\cdot(-2) = 16 +24 = 40\\\\\sqrt{\Delta} = \sqrt{40} = \sqrt{4\cdot10} = 2\sqrt{10}\\\\x_1 = \frac{-b-\sqrt{\Delta}}{2a} = \frac{-4-2\sqrt{10}}{2\cdot3}} = \frac{-2-\sqrt{10}}{3}\\\\x_2 = \frac{-b+\sqrt{\Delta}}{2a} = \frac{-4+2\sqrt{10}}{6} = \frac{-2+\sqrt{10}}{3}[/tex]
Współrzędne wierzchołka:
[tex]W = (p, q)\\\\p = \frac{-b}{2a} = \frac{-4}{2\cdot3} = -\frac{2}{3}\\\\q = \frac{-\Delta}{4a} = -\frac{40}{4\cdot3} = -\frac{10}{3}\\\\W = (-\frac{2}{3}, -\frac{10}{3})[/tex]
