Answer: I am not certain if you mean you purchased cut flowers or plants with roots. If you purchased cut flower stems, they will not grow and should be discarded when the blooms have faded.
If you purchased peony plants growing in containers of soil, then yes, you can plant them in the garden. These are very long lived plants.
A sunny location is best. Allow about three feet width for each plant's mature size and spread. Prepare a wide, deep planting hole for each plant, so the roots have lots of room, loosening the soil and adding organic matter such as compost to enrich it and improve the texture.
To plant, place the peony in the soil so that it is at the same level as it was in the pot, no deeper. Firm the soil around it well, then water deeply to eliminate air pockets. Make sure it is not planted too deeply, because this will prevent it from blooming in the future.
Surround the plant to cover the root zone (but do not place mulch against the stems) with several inches of organic mulch such as shredded bark. Water as needed this summer and fall to supplement rain so that the soil stays evenly moist but not sopping wet.
Each fall, clean away the old stems and leaves after frost kills them back. In early spring, install a peony ring or other support for the peony to grow up through to help it stay upright when it blooms.
Enjoy your peonies!
Q&A Library Searching Tips