Does the quality of your middle school affect the high schools that are willing to accept you?

I'm on my last year in middle school and I just moved so I have to finish that year in a new school. The school I'm zoned for is really bad and you can change it with a special request. Is going to a school with low-quality education going to affect what high school i would be able to get in to? or is it just dependable on my grades??