I am a teen girl. I eat about 1,700 calories a day. Then I burn about 800 calories through exercise. I know you need to eat 1,200 calories to lose weight. Should I eat more so my calorie intake is 2,000 calories? Or does this number just the minimum you can eat to lose and doesn't relate to exercise?
Calorie Count tools are no good for teens, they were designed for the over 21. This tool, from the Baylor College of Medicine, can help you learn how many calories you burn as a teen.
Overweight, ACTIVE (which you clearly are) females should eat at least 1800 to lose weight. I don't have a age/weight/height on you, but for right now I'll presume you are overweight by BMI standards. So eating 1800 would be your absolute minimum. You seem to be very active (or intensely), as most people don't burn 800 through exercise, so yes -- bumping to 2000 would be a good idea.
Unless you are very overweight (BMI 35+) you should shoot for daily deficit of no no more than 250-500 calories (deficit = calories burned (normal + exercise) minus calories eaten.
Overweight, sedentary teen females should eat at least 1500 calories to lose weight. The 1200 thing is the lowest recommended for adult females (over 21) -- but it's too low even for most of them. Especially if they are active, young, or taller than 5'
I went on a diet at the age of 17 and ate 800 calories days I did not exercise and 1200 days I did. I would not do it again. I lost 30lbs in 2 months sure, but only a few months after I ended my diet I gained back the 30 and then some. I'm not 20 and starting again. Counting calories is not bad for a teenager, just don't under eat. Stick to your food pyramid and write down everything you eat and get some exercise every day. Over exercising is also a eating disorder. The goal is to burn more calories than you take in. But remember you burn calories while sleeping, sitting, and every other activity that you do. So don't just think of your exercise as your calories. I have burned over one thousand calories today sleeping and going to work. The biggest thing to remember is to make it a lifestyle, not a "diet" and you are all good :]