From what you describe, your parents cannot claim you on their taxes; because:
-You do not live with them, not even in the summer or school vacations
-You make more than $4000 per year in income and/or they do not provide more than half your support
Even if you claim yourself, you are not eligible for the refundable portion of the American Opportunity Credit, because most of your support comes from FAFSA & loans
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There
are two types of dependents, "Qualifying Children"(QC) and standard ("Qualifying
Relative" in IRS parlance even though they don't have to actually be
related). There is no income limit for a QC but there is an age limit.
A child of a taxpayer can still be a “Qualifying Child” (QC) dependent, regardless of his/her income, if:
1. He is under age 19, or under 24
if a full time student for at least 5 months of the year, or is totally &
permanently disabled
2. He did not provide more than 1/2 his own support. Scholarships are
considered third party support and not as support provided by the student.
3. He lived with the parent
(including temporary absences such as away at school) for more than half
the year
A person can still be an
other dependent (Qualifying relative), if not a Qualifying Child, if he meets the 6
tests for claiming a dependent:
1. Closely Related OR live
with you ALL year
2. His/her gross taxable income for the year must be less than $4,000 (2015)
3. You must have provided
more than 1/2 his support
In either case:
4. He must be a US citizen or resident of the US, Canada
or Mexico
5. He must not file a joint
return with his spouse or be claiming a dependent of his own
6. He must not be the
qualifying child of another taxpayer
