Quadratic Equations - why 'quadratic'?

Factual Questions
1

It’s been 8 years since I’ve taken Algebra, and I’ve forgotten whether I’ve ever known… What does ‘4’ have to do with it? 2nd degree polynomial, 2 solutions…
I suppose that some parabolas have values in all 4 quadrants, but so what?
I can’t believe this question is keeping me up at night.

2

How about this: Quadri– means either 4 or square. A quadrate is a square (which is an object with 4 sides). Quadraticis derived from quadrate, and describes equations that have terms of the second degree, i.e. terms that are squared.