The parents, if the mini were ever used officially by them and had any software
installed, bought music, updated the system, etc, would've used their Apple ID.
So, if through legitimate sources and correctly set-up, or if bought used and set
up with the new owner's information, installed new OS X, and etc, it would have
an Admin account or be accessible by the owner's Apple ID.
Before using suggested links to change an unknown Admin access password,
be sure to check, because if this unit has seen any software update, iTunes,
App Store or Mac App Store access, someone has an account and it may be
that would alter how the computer was used by them, if you change it now.
Also, to update or upgrade System software, and most online store access, does
require a valid payment card to be entered. If the parents are a party to this use,
then seems to reason, they should be in on what to change the new password to.
Good luck & happy computing! ๐