Focus of the parabola is (-5,5) and directrix is y = -1.
Let's assume a point (x,y) on parabola.
According to definition of parabola, the distance between point (x,y) and focus (-5,5) would be same as the distance between the point (x,y) and directrix y = -1.
Hence, option D is correct, i.e. f(x) = one twelfth (x + 5)2 + 2.