Summarize:

Try looking at the refurbished or used laptops that brands and retailers sell for very reduced prices.  Create your own comparison chart of prices and features of several possible laptops, or find and print one from online to show your parents that you've given this a lot of thought and research. Consider what you can do in exchange for your parents buying you a laptop. Promise good grades on your next report card, a certain amount of chores per week or month, or another goal you know your parents would like to see you achieve. Try coming up with a specific goal that you can stick with and achieve. When you talk to your parents, you can say, “I'll get a better grade in English next semester,” or something that you know could use improvement and that you think you can achieve. Think of all the ways that a laptop would make your life easier or more successful. When the time comes to talk to your parents, point out to them your practical reasons to have one, as well as the benefits of a laptop over a desktop, like portability, convenience, and that it doesn't take up space.  For school, think of how you could use a laptop to take notes (if allowed), to bring to study groups or tutoring, or to access online libraries and other reference resources. If you're off to college in the near future, you can point out to your parents that you will need a laptop for notes, research, and to make video calls home!  Some students actually do better in school with laptops if they have a very slow handwriting speed or other difficulty taking notes. If you struggle with this, use this in the argument you bring to your parents. Think of an argument for how you can use a laptop to cultivate useful talents and beneficial hobbies. Want to get into graphic design? Computer coding? Writing? You need a laptop to learn and practice these skills that could later become jobs. Show your parents that there are lots of educational resources for free online that you would be able access on a laptop and have more time and freedom to use than on a school or family computer. Display to your parents that you don't use your current family or personal computer too often, so you won't be on your own laptop all the time. Commit to cutting down on your screen time, if necessary, in advance of talking to your parents, so that you can point out to them your good habits when you sit down to talk. Try getting on the computer for only a half an hour at a time, or only when all your homework is done at the end of the day. Compile all your research, reasoning, and offers for a laptop and write them down neatly or type them up into a document to print out for your parents. Show them you are responsible, have given this a lot of thought, and are willing to stick to your goals to own your own laptop. You can even create your own “contract” or agreement for whatever you offer in exchange for a laptop, so you can track your progress and let your parents hold you to your goals.
With these needs in mind, compare prices on laptops with the features you want. Come up with an offer or bargain. Come up with practical reasons for a laptop. Plan to use the laptop for hobbies and skills. Show moderation in your computer usage. Put your offer in writing.