Then you can add the Z axis back in, which is pretty simple, since you already have the Z values for the first two points, and the third point (the one we just found) has a Z value equal to the first point's (by definition of a parabola)
The parabola in 3D space will always be in the xz plane (where xy is horizontal and the z axis is up and down), but rotated by some angle with respect to the x-axis.
I'm not sure why you're having such difficulty understanding what Zach is trying to do.
If he's talking about mirroring an "endpoint" (so to speak) across the vertex, like you can do in 2D, there's pretty much only one way for that to work in 3D.
@ZachGates Please answer whether any parabola is allowed, or only certain parabolas; and if the latter, which parabolas are excluded from consideration.
@ThomasKwa In a sense? The challenge currently says that you are given the vertex of a parabola in 3D space and another point on the parabola, then asks you if a third, given point is on the parabola. We're discussing restrictions.