Also, the most literal answer "solve quadratic equations" is kind of the most meaningless, what a physicist does with it is different than what a graphic designer does with it. The teacher might be saying they don't know in that context and would rather not lie to individual students that it's super important for them in particular way.
He is exactly where he is supposed to be. They do not want a thinking general population equipped with cognitive tools. That would be a disaster for that set and the end of their long running party.