General form of Parabola with Axis parallel to y axis: (x-a)² = 4k(y-b)

From (0,0), we have a² = -4kb                                                             ----------------------------         A

From (1,0), we have 1+a²-2a = -4kb                                                    ------------------------------      B

From (-2,4), we have 4+a²+4a = 16k - 4kb                                        --------------------------------       C

From A and B,  1-2a = 0, so a = 1/2.

From C and A, 4+4a=16k or 1+a=4k or k=1/4 + a/4 = 3/8. so k = 3/8.

From A, 1/4 = -3b/2  or b = -1/6.

So equation of the parabola is (x - 1/2)² = 4 * (3/8) * (y + 1/6).

RATE ME IF I AM CORRECT