Quadratic relationship is between the speed and force of impact.
If you want to accelerate pedestrian to certain speed you have to pump kinetic energy into him. You do that by applying a force over some distance (distance is how much pedestrian will squish during impact before it starts moving with the car) so to acellerate to double speed, you need to pump in quadruple energy, you need to quadruple the force since squishing distance is the same (until you reach speeds that pulverize pedestrian bones).
Re:Traffic Engineers’ Epic Fail
by GalacticDomin8r on Sunday December 17, 2017 @12:09PM
(#15946560)
I'll make it even easier:
The original data is from https://www.aaafoundation.org/sites/default/files/2011Pedest...
If you look, on page 9, you can see the plots of impact speed vs risk of death. They are clearly non-linear, and they you can also read that they tried various fitting methods for missing data (and quadratic best fit things).
I'm just guessing that you are confused because it does not appear the constant for the x^2 term is >1.