Help! Did i destroy my car?

I have a 2011 corolla with after market speakers, stereo system, amp, and a subwoofer.

The other day my battery died and I bought a new one.

I put one wire into the positive and one wire in to the negative and I started the car.

The car started acting funny. It would shake and make a weird sound like it was about to die especially when the car was stopped or I was making a turn.

I probably had the car on for 30 minutes and drove about 4 miles.

I realized the radio was not working.

When I checked my battery again I noticed that there was another wire that looked like it should go into the positive terminal.

When I connected that wire the radio started working and the car stopped shaking and felt like it went back to normal.

My question is, what was that wire? If it was for the radio and stereo system why would disconnecting it make my car shake and feel like it was about to die?

By driving around about 4 miles and about thirty minutes did I damage my car?

Did I damage the brand new wal-mart battery that I bought?

I really would appreciate all your help!!

It was probably a hot wire for the alternator. You were running straight off the battery, which shouldn't necessarily hurt the car, but it could put a strain on the battery.

It was probably a hot wire for the alternator. You were running straight off the battery, which shouldn't necessarily hurt the car, but it could put a strain on the battery.

Thank you!!