we know that
if the y terms is squared so it opens left or right
Is a Horizontal Parabola, the equation is of the form
(y-k)²=4(p)(x-h)
vertex is (h,k)
and
p is distance from focus to vertex, also distance from vertex to directrix
if p>0, then it opens to the right and directrix is to the left of vertex
if p<0, then it opens to the left and directrix is to the right of vertex
so
(y-1)²=4(4)(x-(-3))
vertex is (-3,1)
4>0 so directrix is to left of vertex
left is in x direction
-3-4=-7
directrix is x=-7
the answer is
x=-7
see the attached figure
