The eqn. of the parabola is (x-1/2)²=(3/2)(y+1/6).

Since the axes is parallel to Y-axis,It's eqn. is of the form

(x-h)²=4a(y-k).Now,Substitute the given points in the eqn. to find a,h,k.

h²=-4ak  ,  (h-1)²=-4ak  ,  (h+2)²=4a(4-k)

Subtracting 1 from 2,we get,h=1/2.So,ak=-1/16 and a(4-k)=25/16

Dividing these two,we get,k=-1/6 and hence,a=3/8.

Thus,the eqn. is (x-1/2)²=(3/2)(y+1/6).

On simplifying,it becomes 2x²-2x-3y=0.