Quadratic phenomena

Definition: A dependent variable (y) that is a quadratic function of an independent variable (x), resulting in y(x) having a U or inverted U shape.

Intriguing hypothesis (to be tested):
y: Number of cliques in a city with high intra-clique cultural diversity
x: Cultural diversity of the city

1. Can you think of any other interesting quadratic phenomena?

2. Why are quadratic phenomena sexier/more convincing than linear phenomena (eg. my grandmother's age vs. crude oil prices)?

3. Are they more convincing because there are fewer quadratic sources of confound than linear sources?

4. Are quadratic phenomena sexier to (straight) men because of their curves? If so, is there a population of (straight) women who find linear phenomena more intriguing? (line = thrusting, pointy, hence more masculine). In this connection, there was a looney tunes animation with narration about a love story between a circle and a line.