Can you apply to a prestigious university if you don't have a high?
Depending on the program and timing, certainly! Master's and Doctor's programs will always take students with a Bachelor's depending on their grades and scores on tests. If you want to transfer from a standard college to an Ivy League, that is a bit harder. Harvard and Yale, for example, will accept transfers so long as they have not completed their second year of college. You need flawless grades (which can be difficult if you get a bad professor. They can be poison). You also need to be VERY impressive. In example, if I had flawless grades I MIGHT get into Yale due to my charity work. There are also non-traditional student routes. You can apply to these universities, but you have to be VERY special. Like Malala at 25 and no longer at college would be one of those non-traditionals to go to Yale (if she hadn't already that is). Other private schools are much easier in comparison. Good grades are preferred, but it is not nearly selective as an Ivy.