Is this the elephant gambit? And how to respond?

Hello all, I have seen this game played by 2 persons back to back this morning and I would like to have more info on how to respond please. I am playing white. Thanks!

What I thought was to take it but then he captured with Qxd5 instead of advancing is e pawn... thus differencing the elephant gambit game I found online.

Just develop calmly with 3.Nc3 driving the queen away and 4.Bc4 if the queen goes to a5 or d6.

Yes, it's the elephant gambit. I am not really familiar with it but after ...Qxd5 you could attack the queen with Nc3 and get a bit of a lead in development. Kingscrusher has done a video on it http://www.youtube.com/watch?v=y43yz3wegXQ but I'm not sure he covers the Qxd5 line. 

i play it al the time and this is how it goes. 1.e4 e5 2.nf3 d5! 3. exd5 e4 4. qe2 qe7 5.nd4 bc5 6. nb3 and white is fine.

Thanks for your comments fellas, I will just play it nicely with Nc3 then. And thanks Kingcrusher20, but I was referencing to the Qxe5 line

Have a good day all :)

Kingcrusher20 in your line, 4...Qe7 blocks the Bishop on f8 so how can you play Bc5 on next move?