I assume you mean quadratics.
I don't exactly know what you mean by "how do they work" but here is what I could think of right now.
Quadratic equations are equations where there is at least one variable raised to the power 2.
The standard form of a quadratic is
Quadratic equations produce a nice curve (a parabola) when graphed.
There are usually two 'roots' or 'zeroes' to a quadratic equation. (roots or zeroes mean answers)
Check this website for more info on quadratic equations.