Why didn't Izuku's mom ask about his quirk?
I can think of a few possible reasons why this would have happened.


Izuku's mother assumed that he developed his ability at some point, but chose not to use it often due to its side effects. In this case, she may not have mentioned it, realizing it may be a sensitive subject.
Izuku has a very close relationship with his mother, and people with these types of relationships can often tell a lot more about each other than most. His mother likely sense that, for whatever reason, he didn't want to talk about his quirk, and decided not to press the issue.
She asked Izuku offscreen, and he deflected her question somehow; which would end up resulting in the same effect as 1. or 2.