How do you catch Rayquaza if you kill it? - Answers

You Can. When you knock out a Pokemon, the Pokemon has fainted and cannot be captured Until you re beat the pokemon league. In the case of one time showing Pokemon (legendaries just like Rayquaza), if you knock it out, you can capture it without restarting the game and going all the way back to the point to capture it. I personally always save the game before I ever battle a legendary Pokemon, and if i successfully capture the Pokemon, i save the game right after i get it to avoid an accidental loss of data.