Hmm. This is a really tricky one.
I'm presuming that your parents buy your food and cook it too. Perhaps you could offer to cook for the family a few times a week? You could make these meals vegan.
Maybe it's too much of a 'shock' to them. I appreciate you might want to just go vegan overnight, but getting your parents on board even a little will probably help. It gives them a chance to consider a change of diet for themselves. For instance if you are attempting to go vegan
no matter what they might try to match the stubbornness like-for-like and in the end no change to your diet happens at all. I've seen this happen a few times.
Perhaps you could suggest week-day or weekend vegetarianism. Even
pescetarianism? That's how I started out. I know it's not at all ideal but if they are meat-lovers then it will be tricky to get them to be receptive - see if you can find a way. You could suggest eating the same meals as them if they just prepare the meat separately: i.e. they make a roast meal, and you can just replace the meat for a nut roast or something. If you can get them to follow your lead this will be an amazing accomplishment. Unless you've got the pocket money to sort out your own meals.
See if you can find their reason for their resistance. Whether it's health (it can be hard to undo the conditioning of the animal agriculture industry), convenience, etc.. You could show them the vegan substitutes for meat and cheese if the word 'vegan' conjures up scary images of endless salads for them. Or explain that a vegan diet is generally cheaper.
It will be easier to try to address their concern if you know the real reason why they feel the way they do. If they are simply resistant because they consider meat a part of their 'culture' then perhaps you could suggest trying out a nearby veggie restaurant, or point out how many famous vegans there are (including President Bill Clinton as well as former Vice President Al Gore). Well done for doing a presentation - serious kudos! But perhaps they would be more open to a documentary? There are so many to choose from.
I hope you find these links useful. Do let us know how you get on, and if you have any further questions just ask!
http://vegyouth.com/choosing-veg/talking-to-your-parents/
Famous vegans and vegetarians:
https://en.wikipedia.org/wiki/List_of_vegans
http://vegan.wikia.com/wiki/Famous_Vegans_and_Vegetarians
http://www.geni.com/projects/Famous-Vegetarians/14487