How do I shift a vertex to establish a single, flat surface on a quad? One thing that I've noticed when drawing quads is that, if a single surface cannot be established using the vertex arrangement (for example, if you add the default plane and raise a single vertex to 1 on the Z-axis), Blender will treat it a quad (subsurf works fine with it and will smooth it out into a hyperbolic surface) but render it as two conjoined tris (prior to the subsurf).

Now, I'm fairly certain that I should avoid this in most cases and would want to fix it if it does occur. In my example above, I could obviously just shift the vertex back to 0 on the Z-axis, because the surface is completely flat. However, if I were to rotate this quad, I would be in a situation where moving the vertex to establish a flat surface would require very precise changes to the X, Y, and Z positions.

I was wondering if there is some feature of Blender or a technique to adjust vertices exactly that the quad is absolutely flat, even if the quad is rotated.

P.S. I apologize for the very technical  and possibly pedantic style of writing. Because I want to ensure the question is communicated clearly, I felt that it was necessary to be scrupulous.
If you only care about planar faces in general, then there's an automatic way for that by selecting Mesh > Clean Up > Make Planar Faces.

If you really want to only move a specific vertex of the quad, you can


move the 3D Cursor to one of the three other vertices (Select the vertex, Shift+S > Cursor to Selected) and switch to Pivot Point > 3D Cursor (. key)
Shift-select all three vertices that should define your plane and should not move
Hit Ctrl+Alt+Space to define a custom Transform Orientation
Select the vertex that you want to move and scale it locally along the Z-axis of the new transform orientation: SZZ 0 Enter