Upgrades are available depending on availability. Some here can help you if you share your flight dates and times; when there's a lot of unsold business class seats, you might get offers during check-in. Those offers might or might not show for you; it's proprietary information as to how they target people for them. Be aware that buying one upgrade reduces the odds of others seeing them, so once you have bought an upgrade for yourself, your parents might not get similar offers. Prices vary from great deals to absurd amounts.
On the Day of Departure (DoD) you can go to the airport and get a spread of options for miles / miles + cash and straight cash upgrades if the seats are available. Again, they might not be.