It depends on the teacher, level of the course, and what will be missed during your absence.
I have had a pre-calculus teacher deny my request to go to a MANDATORY orchestra event a few weeks ago just because he could (and I soon transferred out of his class), but more often than not, teachers will be understanding of the trip.
Teachers, though, may be a bit less willing if the classes you are leaving are AP classes compared to "blowoff electives." Some AP classes may have attendance policies, so I suggest that you re-check the syllabus for your classes if you're concerned about that.
Depending on what will be missed, you could be in for an easy return or a few days of torture. If you will be missing state exams, expect to be missing even more classes to make up these tests, and most schools do have a policy on how long you have to do your work, if any, before it counts as a zero. It would be a good idea to collaborate with your teachers to see what you will be missing, when you should turn in your make-up work, and when you should make up and tests, if any, before you leave for your vacation.
Here's an example of some of the work I've received when I went on a vacation in April last year for three days:
H Algebra II: Complete a homework and notes packet for when I return to school. Make up a test.
Biology: Complete a lesson packet for the day before I leave.
English: Complete a grammar packet and essay for the day I return.
H World Affairs: Study for Asia exam and get notes on what I've missed.
Orchestra: Nome (we all were gone on this trip)
H German: Complete a few book pages and make up a quiz.