[tex]a)\\\\y=x^2 -2x-3\\\\a=1,\ \ b=-2\ \ c=-3 \\\\miejsca\ zerowe:\\\\\Delta =b^2-4ac=(-2)^2-4*1*(-3)=4+12=16\\\\\sqrt{\Delta }=\sqrt{16}=4\\\\x_{1}=\frac{-b-\sqrt{\Delta }}{2a}=\frac{2-4}{2*1}=\frac{-2}{2}=-1\\\\x_{2}=\frac{-b+\sqrt{\Delta }}{2a}=\frac{2+4}{2*1}=\frac{6}{2}=3[/tex]
[tex]wierzcholek\ paraboli :\ \ w(p,q)\\\\p=\frac{-b}{2a}=\frac{2}{2}=1\\\\q=\frac{-\Delta }{4a}=\frac{-16}{4}=-4\\\\W(1,-4)\\\\\\\\przeciecie\ z\ osia\ OY\\\\x=0\\y=x^2 -2x-3=0^2-2*0-3=-3\\\(0,-3)[/tex]
[tex]b)\\\\y=-\frac{1}{2}x^2 +2x+6\\\\a= -\frac{1}{2},\ \ b= 2\ \ c=6 \\\\miejsca\ zerowe:\\\\\Delta =b^2-4ac=2^2-4* ( -\frac{1}{2})*6= 4+12=16\\\\\sqrt{\Delta }=\sqrt{16}=4\\\\x_{1}=\frac{-b-\sqrt{\Delta }}{2a}=\frac{-2-4}{2* (-\frac{1}{2})}=\frac{-6}{-1}=6\\\\x_{2}=\frac{-b+\sqrt{\Delta }}{2a}=\frac{-2+4}{2* (-\frac{1}{2})}=\frac{2}{-1}=-2[/tex]
[tex]wierzcholek\ paraboli :\ \ w(p,q)\\\\p=\frac{-b}{2a}=\frac{-2}{2*(-\frac{1}{2})}= \frac{-2}{-1}=2\\\\q=\frac{-\Delta }{4a}=\frac{-16}{4*(-\frac{1}{2})} = \frac{-16}{-2}=8\\\\W(2,8)\\\\\\\\przeciecie\ z\ osia\ OY\\\\x=0\\y=-\frac{1}{2}x^2 +2x+6=-\frac{1}{2}*0^2+2*0+6=6\\\(0,6)[/tex]