Which sort of lets me with one more question, to do with the reason for y = 2x^2 - 2x + 113/102 (my basic equation wrt to the thus constants), in the sense that it's a parabola. What's going on there?
Hopefully, another good answer, so that the enchantment of the question is forever lost.
https://en.wikipedia.org/wiki/Conic_section
https://en.wikipedia.org/wiki/Paraboloid