I have been a vegetarian for 15 years now, since I was eight years old. I came home from a school camp where I had seen some pretty eye opening going ons. I told mum and dad about my choice and they were more than supportive. If an eight year old can do it, anyone can. If I were you I would sit down and have a pretty indepth chat with your parents, do a bit of research, know your stuff so they can see that your serious and its not a fad. Search the net for veg recipies and ask if you can cook one night for the family if your mum and dad will support your for the other 6 nights or something.
And if you need to, tell them its your religion (i think buddhists don't eat meat, but don't ask me i'd have no clue lol)
The #1 reason I became a vegetarian is because I am a Buddhist in training... so yes 99% of Buddhists are vegetarian. A few are vegans. #2 reason was health. #1 reason for becoming a vegan was for the animals. (I hate admitting I initially didn't go vegetarian for the animals, but I think I have made up for it by going vegan )