Norton Utilities has a trash cache that is not user deletable as I recall.

Also, if you're really suspicious, you can get little programs that can record every keystroke inputted on a computer. So then you can tell what they are searching for. I can't give you a url for this, because I must have read it in mac addict/mac world a year or two ago, but they are out there. Little free programs that do that. Innocuous and hard to find, they pretend to be a system extension and write a log to some place you designate.

Edit:

In addition, although I certainly have no right to interfere with your parenting...but being a teenager myself, I think I could safely say that your child/children may not really appreciate your snooping around on what they've searched. But, ack, none of my business.