Standard form of the parabola function: (y-k) = a(x-h)²
vertex (h,k)==> vertex (2,-5) [given]. Now plug==> y+5 =a(x-2)²
To calculate a, plug in the equation the coordinates of A(3,4)
4+5 = a(3-2)² ==> 9=a
Finally the equation is f(x) = y+5 = 9(x-2) or y = 9(x-2)² -5
Or f(x) =y = 9x² - 36x + 3
