Ornamental sweet potato (Ipomoea batatas), grown primarily for its purple, chartreuse, or variegated foliage, is a true sweet potato. As such, the tubers it forms are edible. Popular varieties like 'Marguerite' have small, round tubers, while varieties like 'Blackie' have longer, narrower tubers.
However, the texture and flavor of tubers from ornamental sweet potato vine will not be as good as varieties developed specifically as a vegetable. If you're looking for flavor, you'd be better off with the garden types for stocking your kitchen pantry. Also, if you sprayed the ornamental type with pesticides not labeled for vegetables, the tubers should not be used as a food.
If you don't like the taste of the tubers, you can try out the leaves—they're edible, too! They are full of vitamins and antioxidants and are also a good source of fiber. Raw sweet potato leaves are fairly bitter like spinach, but lose their sharp flavor when boiled.
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Whether you want to eat them or not, it's always worth keeping the tubers. You can save them like bulbs and plant them in containers the next spring. You can store them in a box in a cool place throughout the winter.
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You can make cuttings, also known as sweet potato slips, from store-bought potatoes and ornamental potatoes; however, you may not know which variety you're growing. Instead, buy your first set of slips from a garden store to ensure you get a type that will grow well in your area, then use a few of those potatoes to make slips for next year. Or, be sure to keep the plant tag from the vines you buy from the nursery so you remember which variety you have in your containers.
To start, set a sweet potato in a jar of water. Leave it in a warm, sunny spot. It will send out roots and leaves within two weeks. Once they've had a chance to grow a few inches long, cut off pieces and place these cuttings in another jar of water. Wait another 1-2 weeks for them to root. They're now ready to be planted!
Sweet potato vine does best in full sun and warm weather. Some of the older varieties may grace your garden with a few sporadic lavender blooms that look like a slightly more tubular morning glory, and for good reason—sweet potato vine is a close cousin to this common annual vine. Sweet potato vine does extremely well in containers and is a common spiller in a container garden.