It's a really big assumption to make that she has a black eye so she must be being abused at home. If she comes to school all bruised up on a regular basis, then you could probably assume she's being abused. However, you don't know for sure if she is and if she is, by whom.
If she is a friend, then I would take her aside - somewhere no one else can hear your conversation - and ask her if someone hurt her and if so, did she need medical attention. Tell her that you are concerned about her and want to help.
It could be this was a sibling spat - she got on her brother's nerves and he punched her. It could be that she has a boyfriend no one knows about and he punched her. It could be that she fell and got a black eye. This last example happened to me where I blacked out and hit the toilet paper holder built into the vanity, broke it and got a bruised face out of the experience.
Ask her about it, listen to what she is telling you and then try and make a good decision about this.
