When you say "downloaded", I am assuming you meant you've installed it from the App Store. Anyway, go to your home screen if you have iOS 7, swipe downward to reveal the spotlight search function. Type in" Facebook", when you see it listed under "Applications", tap on it. If it is not listed, go to the App Store and install it.
This happened to me the other day. When I did spotlight it didn't show up but when I went to the App Store, it said open & I clicked it & nothing happened. I had to reboot my phone twice & it came back. Hope you find it!