What practical application does a quadratic equation have, apart from passing exams?

Arc motion of a projectile, tensor strength of bridges, melting points of proteins, equilibrium calculations of a chemical mixture.

Just so you know I'm not making up the thermal stability of proteins, look at the quadratic curves and quadratic equations and this paper, where "x" is temperature:

https://dasher.wustl.edu/bio5357/reading/biopoly-2...

I read this exact paper last year in biophysical chemistry class.

Most things in the physical world move in a quadratic.

GPS Satellites, orbiters, projectiles, power curves for engines, etc.

As well as a lot of business, such as best fit, weighted average, profit, etc.

I know a few jobs that don't need math:

making change at a gas station or fast food.

Examples here: https://www.mathsisfun.com/algebra/quadratic-equat...

But the real purpose of most of what is taught in school is to make you learn how to think.

If you have struggled, but managed to work through learning quadratric equations, you have improved your general mental self-discipline and reasoning skills. This equips you to deal with problems that will come up in the future, even if they have nothing to do with quadratic equations.

absolutely none