Filming video kills battery on iPhone 5

Granted, the battery life on my iPhone 5 isn't stellar to begin with but if I film a video it kills the battery quickly (especially if the battery is low to begin with). For instance yesterday, battery was at 35% and I opened the camera app and made a video. The video lasted 9 seconds then the phone shut down because the battery was too low. Today, battery was at 53% and I received a FaceTime call. The call lasted 20-30 seconds then I noticed that the battery was down to 14% so I hung up the call. Both times I was on LTE although not sure if that would make a difference.

Does this happen to anyone else? Is this something Apple would consider to under warranty under my Apple Care?