[tex]a) f(x) = x^{2} -2x+4\\f(x)+?=x^{2} -2x+?+4\\f(x) +?=x^{2} -2x+1+4\\f(x)+1=x^{2} -2x+1+4\\f(x) +1=(x-1)^{2} +4\\f(x) = (x-1)^{2}+4-1\\f(x) = (x-1)^{2}+3[/tex]
[tex]b) f(x) = -2(x^{2} -\frac{1}{2} x)-1\\f(x) +?=-2(x^{2} -\frac{1}{2}x+?)-1\\f(x) +?=-2(x^{2} -\frac{1}{2}x+\frac{1}{16})-1\\f(x) -2*\frac{1}{16}=-2(x^{2} -\frac{1}{2}x+\frac{1}{16})-1\\f(x)-\frac{1}{8}=-2(x^{2} -\frac{1}{2}x + \frac{1}{16})-1\\f(x) =-2(x-\frac{1}{4})^{2}-1\\f(x) =-2(x-\frac{1}{4})^{2} -1+\frac{1}{8}\\f(x) =-2(x-\frac{1}{4})^{2} -\frac{7}{8} \\[/tex]
[tex]c) f(x) -x^{2} -z+4\\f(x) +?=-x^{2} -x+?+4\\f(x) +?=-x^{2} -x-\frac{1}{4}+4\\f(x) -\frac{1}{4}=-x^{2} -x-\frac{1}{4}+4\\f(x) -\frac{1}{4}=-(x^{2} +x+\frac{1}{4})+4\\f(x) -\frac{1}{4}=-(x+\frac{1}{2}^{2}+4\\f(x) =-(x+\frac{1}{2})^{2} +4+\frac{1}{4} \\f(x) =-(x+\frac{1}{2})^{2}+\frac{17}{4}[/tex]
[tex]d) f(x) \frac{3}{4}x^{2} +\frac{1}{2}x -8\\0=\frac{3}{4}x^{2} +\frac{1}{2}x -8\\\frac{3}{4}x^{2} +\frac{1}{2}x-8=0\\3x^{2} +2x-32=0\\x=\frac{-2+\sqrt{2^{2}-4*3*(-32) } }{2*3}\\x=\frac{-2+\sqrt{4-4*3*(-32)} }{2*3}\\x=\frac{-2+\sqrt{388} }{6}\\x=\frac{-2+2\sqrt{97} }{6}\\x=\frac{-2+2\sqrt{97} }{6} x= \frac{-2-2\sqrt{97} }{6}\\x=\frac{-1+\sqrt{97} }{3} x=\frac{-2-2\sqrt{97} }{6}\\x_{1} =\frac{-1-\sqrt{97} }{3} , x_{2} =\frac{-1+\sqrt{97} }{3}[/tex]
Mam nadzieję, że pomogłam, pozdrawiam :)
