Wzory:
[tex]W=(p,q)\\f(x)=a(x-p)^2+q\\f(x)=ax^2+bx+c[/tex]
Rozwiązanie:
[tex]x=3\\y=4\\p=-3\\q=2[/tex]
[tex]f(3)=a(3-(-3))^2+2\\4=a(3+3)^2+2\\4=a\cdot6^2+2\\4=a\cdot36+2\\4-2=36a\\2=36a\quad|:36\\a=\dfrac{2}{36}\\a=\dfrac{1}{18}[/tex]
[tex]f(x)=\dfrac{1}{18}(x-(-3))^2+2\\f(x)=\dfrac{1}{18}(x+3)^2+2\\f(x)=\dfrac{1}{18}(x^2+6x+9)+2\\f(x)=\dfrac{1}{18}x^2+\dfrac{6}{18}x+\dfrac{9}{18}+2\\f(x)=\dfrac{1}{18}x^2+\dfrac{1}{3}x+\dfrac{1}{2}+2\\f(x)=\dfrac{1}{18}x^2+\dfrac{1}{3}x+2\dfrac{1}{2}[/tex]