Parents able to track iPhone?

Could be anything (not just iphone). But the short answer to your question. No. There are apps though that can track your location and are meant to do so (e.g. Loopt) but only when the app has been opened... maybe there are other apps that can do it without being constantly open.

neuroanatomist wrote:
https://familymap.wireless.att.com/finder-att-family/welcome.htm

I'm on the two phone trial of this service hoping that it would help if I lost another iPhone but so far the service seems useless as it has an accuracy of only 1.2 miles on a good day.

Maybe she implanted a lowjack in you while you slept, and it's not the phone. Do you have any sore spots from an injection on your neck?

This service is just based on tower info and has been around for a long time (use to be free). Use to use it way before the iPhone.

It doesn't require anything on the phone as it is just based off the fact the cell company knows where you are and thus can provide a way for the parent (or owner of account) to check.

There is software available that will allow them to see text messages, who you call, etc if they want to. The best thing is to be honest with your parents. This will show that you are mature and trust them.