First, let her know you share her goals- your education is the most important thing and you must take care of your family responsibilities. Show her that basketball will not interfere with this but will, instead, help.

Physical fitness is not only important for its own sake but for mental clarity. This helps study, it doesn’t interfere with it.

Happiness- you will be better at everything else if you are happy. If you are disgruntled it will show in other areas of your life. You won’t intentionally sabotage your work, but if you aren’t happy it is likely to show up.

Companionship- if you are going to practice with others let her know that socialization is important for kids your age. Learning lessons like good sportsmanship and fairness and cooperation are as important as geography.

Well roundedness- People value those with wider experience. Showing colleges that you are more than just a study machine will make you a more attractive prospect.

Bargain- if she still says no, bargain. Maybe offer to do it only for a trial period to make sure your grades don’t suffer. Or offer to meet agreed requirements such as two hours of study and walking the pet puma before you can play.