[tex]zad.3\\\\y=2x^{2} -5x-3~~postac~~ogolna\\\\a=2,~~b=-5,~~c=-3\\\Delta=x^{2} -4ac\\\\\Delta=(-5)^{2}-4\cdot 2\cdot (-3)=25+24=49\\\\\sqrt{\Delta} =\sqrt{49} =7\\\\\\x_{1} =\dfrac{-b-\sqrt{\Delta} }{2a} ~~\lor ~~x_{2} =\dfrac{-b+\sqrt{\Delta} }{2a}\\\\x_{1} =\dfrac{5-7}{4} =\dfrac{-2}{4} =-\dfrac{1}{2} ~~\lor~~x_{2}= \dfrac{5+7}{4}=\dfrac{12}{4} =3\\\\\\Postac~~iloczynowa\\y=a\cdot (x-x_{1} )\cdot (x-x_{2} )~~gdy~~\Delta >0\\y=a\cdot (x-x_{0} )^{2} ~~gdy~~\Delta=0\\\\[/tex]
[tex]y=2\cdot (x+\dfrac{1}{2} )\cdot (x-3)~~-postac~~iloczynowa~~funkcji~~kwadratowej \\\\\\Postac~~kanonicza:\\\\y=a\cdot (x-p)^{2} +q~~~~gdzie ~~p=\dfrac{-b}{2a} ,~~q=\dfrac{-\Delta}{4a} \\\\p=\dfrac{5}{4} =1\dfrac{1}{4} \\\\q=\dfrac{-49}{16} =-3\dfrac{1}{16} \\\\y=2\cdot (x-1\dfrac{1}{4} )^{2} -3\dfrac{1}{16}~~postac~~kanonicza~~funkcji~~kwadratowej[/tex]
