Actually, Listen to Steve, he's wise!
I actually managed to persuade my parents to get a DC14 Origin today. Show your parents your report card if it's good. Offer to do chores and clean your room etc.
Help your mum and let her relax more than usual.
As for Dad, ask him when he is in a good mood such as payday.
If he is given a gift by someone, he may be happy and be in the giving mood so ask then

show your parents that you want this badly and work very hard.
You might find this hard but think of the Numatic.
Tell them the advantages about it so that they are more convinced
Tell your parents how it will benefit them instead of you.
Say you will not have any more vacs for a while and pay them for it because if not then they may not believe you next time
Google more tips
PS Ask your parents "What can I do to have this?"
Don't yell, slam doors argue or fold your arms, Go with the flow of your parents.
Sell a vac quickly on eBay or Gumtree for example...