Parabola Equations and the related Coordinates

I put this together partly because I’ve been thinking about: Vieta Formula Brainstorming but mostly because I haven’t seen it elsewhere.  The symmetry is more obvious when everything is on one diagram as well as the interesting correspondences once everything is in terms of roots. 

Background: from the Vieta formulas we already have the correspondence between coefficients in the standard form and the root:   b = - (p+q) and c = pq.  

Also the vertex form is particularly elegant looking because its position neutral.

Standard Form

Root Form

Vertex Form