[tex]7a)\\\\ f(x)=-3(x+2)^2-5\\\\postac\ ogolna:\\ f(x)=ax^2+bx+c\\\\f(x)=-3(x+2)^2-5=-3(x^2+4x+4)-5=-3 x^2-12x-12-5=\\\\=-3 x^2-12x-17[/tex]
[tex]b)\\\\ g(x)=2x^2+7x+3\\\\postac\ iloczynowa:\\\\g(x)=a(x-x_{1})(x-x_{2})\\\\a=2,\ \ b=7,\ \ c=3\\\\\Delta =b^2-4ac=7^2-4 *2*3=49-24=25\\\\\sqrt{25}=5\\\\x_{1}=\frac{-b-\sqrt{\Delta }}{2a}=\frac{-7-5}{2*2}=\frac{-12}{4}=-3[/tex]
[tex]x_{2}=\frac{-b+\sqrt{\Delta }}{2a}=\frac{-7+5}{2*2}=\frac{- 2}{4}= -\frac{1}{2}\\\\\\g(x)=7(x+3)(x+\frac{1}{2})[/tex]
[tex]c)\\\\ h(x)= -2(x-1)(x-5)\\\\postac\ kanoniczna:\\\\y=a(x-p)^2+q\\\\ h(x)=-2(x^2-5x-x+5)=-2(x^2-6x +5)=-2x^2+12x-10\\\\a=-2,\ \ b=12,\ \ c=-10 \\\\\Delta =b^2-4ac= 12^2-4*(-2)*(-10)=144--80=64\\\\p=\frac{-b}{2a}=\frac{-12}{2*(-2)}=\frac{-12}{-4}=3q=\frac{-\Delta }{4a}=\frac{-64}{4*(-2)}=\frac{-64}{-8}=8[/tex]
[tex]q=\frac{-\Delta }{4a}=\frac{-64}{4*(-2)}=\frac{-64}{-8}=8 \\\\\\h(x)=-2(x-3)^2+8[/tex]
