What is the formula for a parabola opening to the left or right in terms of Y?

It is easy ya. Any parabola with vertex h,k and opening left ward will be (y--k)^2 = --4 a (x--h)
As the vertex is given as h = --1 and k = 0 we get the modified form as y^2 = -4a(x+1)
The two points on the parabola cannot be as given by you. Only the y coordinate will have + and --ve and more over the x co ordinate cannot be +ve as the vertex itself is at --1 on Xaxis.
Now as it passes through (-5,-3) and (-5,3) satisfying the equation, we get 9 = --4a*---4 So a = 9/16
So the equation of the parabola will be y^2 = --9/4(x+1)
Note: Here after give the valid details.

The equation of a parabola that opens sideways is of the form:

ay² + by + c = x

Whether it opens left or right depends on whether a is positive or negative.

Plug in the three points (1, 0); (5, 3); and (5, -3).  You will have three equations in three unknowns.
0a + 0b + c = 1
9a + 3b + c = 5
9a - 3b + c = 5

Solving we get:
a = 4/9; b = 0; c = 1

And we have:

(4/9)y² + 1 = x
________

I see that D.W. answered correctly ahead of me.  And she is right.  The second parabola is impossible.

Thx!