Where did edward reveal himself as a vampire?

Bella finds out Edward is a vampire the day that her and her school friends go to La Push and she meets Jacob for the first time. Bella knows he knows more about the Cullens, so she tricks Jacob into telling her by flirting. He tells her that they are called "the cold ones" or you could call them vampires. He explains that the Cullens are the cold ones and then, after some research at home, Bella is convinced that Edward is in fact a vampire.