I am 25, live with my parents, they paid for my living expenses, but I made over $10,000 in 2017. I was a student for 3 months, can my parents claim me on their taxes?

No your parents cannot claim you as a dependent on their tax return, due to your age and gross income of $4,050 or more.  You no longer qualify under the Qualifying Child rules since you are older than 23 and you do not qualify under the Qualifying Relative rules since your income is greater than $4,050

Edit answer - change 4,060 to 4,050

Ok thank you! I just wanted to make sure cause my dad told me to hold off on filing since he gets more to claim me, he wanted to find out if he could still.