Why didn't Izuku's mom ask about his quirk? Izuku was quirkless before, but then he got One For All. His mom saw him use his quirk in the Sports Festival, but she never asked him how he got his quirk. And Izuku told All Might that he hadn't told anyone about One For All, not even his mom. Yet, his mom never asked him about his quirk. Why didn't she say anything?
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.