[tex]y=ax^2+bx+c\\\\a=1,\ \ \ b=3,\ \ \ c=-4\\\\ y=x^2 +3x-4\\\\wierzcholek\ paraboli :\ \ \ W=(p,q)\\\\\Delta =b^2-4ac=3^2-4*1*(-4)=9+16=25\\\\p=\frac{-b}{2a}=-\frac{ 3}{2}\\\\q=\frac{-\Delta }{4a}=-\frac{ 25}{4}\\\\W=(-\frac{3}{2};-\frac{25}{4} )[/tex]
[tex]b)\\\\a=-2,\ \ \ b=-4,\ \ \ c= \frac{1}{2}\\\\ y=-2x^2 -4x+\frac{1}{2} \\\\\Delta =b^2-4ac= (-4)^2-4* (-2)* \frac{1}{2}=16+4=20\\\\p=\frac{-b}{2a}= \frac{4}{2*(-2)}=-\frac{4}{4}=-1\\\\q=\frac{-\Delta }{4a}= \frac{ -20}{4*(-2)}=\frac{-20}{-8}=\frac{5}{2}\\\\W=(-1; \frac{ 5}{2} )[/tex]
[tex]c)\\\\a= \frac{1}{2},\ \ \ b= 0,\ \ \ c= 5 \\\\ y= \frac{1}{2}x^2+0x+5=\frac{1}{2}x^2+5 \\\\\Delta =b^2-4ac= 0^2-4* \frac{1}{2}*5=-10\\\\p=\frac{-b}{2a}= \frac{0}{2* \frac{1}{2}}=0\\\\q=\frac{-\Delta }{4a}= \frac{ 10}{4* \frac{1}{2}}=\frac{ 10}{2}= 5\\\\W=(0; 5)[/tex]
[tex]d)\\\\a= -3,\ \ \ b= 15,\ \ \ c= 0\\\\ y=-3x^2+15x+0=-3x^2+15x\\\\\Delta =b^2-4ac= 15^2-4* -3*0=225\\\\p=\frac{-b}{2a}= \frac{-15}{2 *(-3)}= \frac{-15}{-6}= \frac{5}{2}\\\\q=\frac{-\Delta }{4a}= \frac{-225}{4* (-3)}=\frac{-225}{-12}= \frac{75}{4}\\\\W=( \frac{5}{2}; \frac{7 5}{4})[/tex]
[tex]e)\\\\a= 7,\ \ \ b=0,\ \ \ c= 0\\\\ y=7x^2+0x+0=7x^2\\\\\Delta =b^2-4ac= 0^2-4*7 *0=0\\\\p=\frac{-b}{2a}= \frac{0}{2* 7}= 0\\\\ q=\frac{-\Delta }{4a}= \frac{0 }{4*7}=\0\\\\W=( 0; 0 )[/tex]
