I'm a foster parents. How do i answer if I have an agreement to carried child. He was in my home for six months.

If you have paperwork by an authorized placement agency or a judge then you have an agreement. Combine the paperwork and the child in your home for more than half the year, then you have met one of the dependent requirements. 

See  Publication 501 - Internal Revenue Service pages 12 and 13 for the full set of requirements.