Negative questions can be used to:

=> Confirm that something is true or has happened. You are assuming something is true and you are just checking.
Example: You didn't tell Ted we think he's a lousy boss, did you? (Expected answer: No, I didn't).

=> Express surprise that something hasn't happened
Example: Haven't you mailed that letter yet? (Note that this can often express annoyance. The person asking the question is annoyed that the other person did not do something).

=> Offer a polite invitation
Examples: Won't you come in? Wouldn't you like some coffee?

Study these examples for ways to answer negative questions:

Didn't you see the car coming?
- Yes, I did. (Do not just say "yes" in response to this type of question. Give a complete answer: "Yes, I did.").
- No, I didn't. (You may also say just "no" without "I didn't.")

Aren't you hungry?
- Yes, I am. I Yes, I'm starving!
- No, I'm not. I No, I just had breakfast.

Won't you sit down?
- Yes, thank you.
- No, I've only got a minute.

You're not tired after your trip?
- Yes, I am tired. (Do not just say "yes.")
- No, I'm not tired. (Note here that you're saying "No ... " even though you are agreeing with the person who asked the question. You're confirming that you're not tired.)