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The job of the battery is to supply the energy needed to start the car and a smoothing action for the output of the alternator.
It sounds like yours is doing neither.
Replace it with a quality brand.
I thought I did send that I accepted your answer but I would like to add some information. I am going to replace the battery, but the car will start now without being jumped. When it cuts off it is like some thing was disconnected. So, that made me think it was a connection problem, not just a battery problem. Give me your thoughts, and I will make sure I click the accept answer.