I believe you can. But you need to install some 3rd party app(s) on your childs (and possibly your) phone. Which one I'm not sure. I remember a couple years ago there was talk around of being able to do what you're asking. I never did it however.
Possibly someone else has more current and accurate info.
I recommend family locator. Not quite sure if it works on the iPhone to be honest, but it works on most phones and will keep track of your child wherever they go. You have to pay for that service, if you want something else you'll have to shop around in the Play Store or App Store. Call VZW if you want to try out family locator.
You don't need family locator or 3rd party apps. Just set up an icloud account linked to it and you can track it. Go to icloud.com for info. Its a feature of iPhones.