In my experience, honesty goes a long way when it comes to Apple. My Macbook Air had a battery issue since the day I unboxed it (buzzed very loud when charging and held only about 2.5 hours on a good day). Because I was moving countries to start university at the same time, I had no time to send it back to Apple and wait for a replacement, so I just put up with it. When things calmed down a bit, I brought it into the Apple Store and they offered to change the battery under warranty - only downside: I had to let go of the computer for 3 WEEKS (!!), which was impossible during term time. So, I never got it done and kept using the battery, which I knew was faulty. In a sense it was my own fault, when the battery then completely blew up and dislocated the keyboard and trackpad 3 years later.
I went back to Apple in my last week of remaining Apple Care and told them, that I had been offered the battery replacement years ago, but that I never took them up on it, because I couldn't be 3 weeks without the computer while studying and working. They reminded me that batteries were consumable and not necessarily covered under Apple Care, especially after 3 years of daily usage... but in a gesture of good will they would replace it for me nevertheless.
I doubt I would have gotten the same result if I had gone in there all upset telling them "My battery suddenly blew up and I don't know why, I didn't do anything." ... They would have probably just said "Yeah, it's a 3 year old battery, pay for the replacement or get lost."
If I were you, I'd put on a more remorseful attitude: I'd emphasize that I'm a high school student and spent all my savings from my summer jobs on my first Mac, because I love Apple so much. Unfortunately it was only enough money for a used model that turned out to have a graphics fault. Since there are various recalls going round right now, I was wondering if this machine was covered too or if they could help me out at all? I feel really stupid wasting all my hard-earned money on a broken Mac, but I was just so excited for it. I learned my lesson though: never again from Craigslist.
I feel with such a remorseful and honest approach they might be more willing to help you out on their discretion.