How should I apologize to my parents?

I am 14M and I just had an argument few hours ago with my parents. It was before dinner, and we got very heated and I told my mom to “shut up”. I didn’t mean it but it just slipped out because I was so angry.

At dinner, when things settled, I tried to apologize to them but they said they grounded me from going outside and playing with my friends. When I tried to apologize, they said they have no reason to be nice to me or do anything for me because I was being rude and disrespectful to them.

How and when should I apologize again?