Współrzędne wierzchołka funkcji kwadratowej to (p,q), gdzie [tex]p=-\frac{b}{2a} , q=-\frac{\Delta}{4a}[/tex]
a)
[tex]y = -12x^2+8x+4\\a = -12, b = 8, c = 4\\p = -\frac{8}{-24}=\frac{1}{3} \\ q = -\frac{84 + 192 }{-48}=\frac{276}{48}= 5\frac{36}{48}=5\frac{3}{4} \\ (p,q)=(\frac{1}{3},5\frac{3}{4})[/tex]
b)
[tex]y = -\frac{3}{4}x^{2}+7x+2\\\\ p= -\frac{7}{-\frac{6}{4}} =-7*(-\frac{4}{6})=\frac{28}{6}=4\frac{4}{6} =4\frac{2}{3} \\q = -\frac{49-4*-\frac{3}{4}*2}{4*\frac{3}{4}}=\frac{49+6}{3}=\frac{55}{3}=18\frac{1}{3}[/tex]
c)
[tex]y = 2\frac{1}{5} x^2 -2x + \frac{3}{2} \\y = 2.2x^2-2x-1.5\\p=-\frac{-2}{2.2*2}=\frac{2}{4.4}=\frac{2}{\frac{44}{10}}=2*\frac{10}{44}=\frac{20}{44}=\frac{5}{11} \\ q=-\frac{4-4*2.2*(-1.5)}{8.8}=\frac{4+13.2}{8.8}=\frac{172}{10}*\frac{10}{88}=\frac{172}{88}=1\frac{84}{88}=1\frac{21}{22}[/tex]
d)
[tex]y=\frac{3}{7} x^2 + \frac{1}{5}x+\frac{2}{5} \\ p=-\frac{\frac{1}{5}}{\frac{6}{7}} =-\frac{1}{5} *\frac{7}{6}=-\frac{7}{30}\\ q=-\frac{\frac{1}{25}-4*\frac{3}{7}*\frac{2}{5}}{\frac{12}{7}}=-\frac{\frac{1}{25}-\frac{24}{35}}{\frac{12}{7}} =-\frac{\frac{7}{175}-\frac{120}{175}}{\frac{12}{7}}=-\frac{-\frac{113}{175}}{\frac{12}{7}}=\frac{113}{175}*\frac{7}{12}=\frac{113}{25} *\frac{1}{12}=\frac{113}{300}[/tex]
