The equation of the parabola is given as:

(x-h)^2 = 4p (y-k)

where, 4p is the length of latus rectum, which is equal to length of line segment joining the two given points (-4,1) and (2,1):

4p = sqrt [(-4-2)^2 + 0] = 6 

and p= 6/4= 3/2

and focus is the mid point of the latus rectum, so focus: (-1,1)

the parabola is vertical, since latus rectum lies on y=1 line, and vertex (h,k) = (-1,1+3/2) = (-1, 5/2)    (p units up from y-axis)

using all these parameters, the equation of parabola will be

-(x+1)^2 = 6 (y-5/2)