How do I convince my parents to get me a cat?

Tell your mother that you have been responsible every day, and ask her to really think about it this time, and that you will do all the work of the cat (Litter, food, water, ect.). For the next few days, do all your work, and maybe a little more. Then talk to your mom again. Ask her if she was thinking about it and ask her what she thought. You could make a plan to go to the animal shelter sometime and, when you talk to your mother, have the trip all planned out.