Answer: Your plant is called Cavendish Banana. It's more decorative than something you'd expect fruit from, but it is very tropical looking.
Bananas are not a tree but an herb. They need well-drained soil and frequent water. Growth virtually shuts down below 55 degrees Fahrenheit, and at that time, very little moisture is required to sustain them. But when actively growing, this herb is very thirsty.
Plant your banana in well-drained soil rich in humus in full sunshine. Bananas can be foliar fed with a balanced, soluble fertilizer such as 10-10-10 every 2-3 weeks during the growing season.
The average mild frost will almost never kill the corm and roots but the tender leaves will usually freeze unless they can be covered or otherwise protected. If the top dies down with frost, trim them off at ground level and the roots will send up healthy new growth.
In summary, grow well-established bananas in full sun in well-drained soil rich in organic material. Water and feed them well during warm weather, let the plants rest during the winter.
Enjoy your new plant.
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