6:37 AM
@K.Krull Ah, I learnt quadratic equations in middle school algebra but I forgot what it exactly is. So I ask Wikipedia that says the following: "In mathematics, the term quadratic describes something that pertains to squares, to the operation of squaring, to terms of the second degree, or equations or formulas that involve such terms. Quadratus is Latin for square."
I do not remember earlier when I skimmed Cha 4, section 1,2, I did not see any equation with square terms. Perhaps I must skimmed again. Anyway I think the curve is NOT exponential, because MOS is not related to diodes or P-N junctions, which is modelled using exponential functions of Euler number e and Boltzman constant k

7:07 AM
As Jaeger says, the "pinch-off locus", which separates the linear and saturated region, is the series of points at different Vgs, each points of which is the intersection of two equations (an example at Vgs = 3V), as illustrated below:
At the end of the NMOS lecture, Pro Jaeger gives a summary of the mathematical model of NMOS with a couple of equations which the miserable struggling students (Thank God not me!) must memorize by heart. The equations are integral, so should not be considered as quadratic, I think.
Afternoon tea time! Nice chatting. Chat you later.