Congratulations, you have peonies! They're pretty easy to take care of, just keep the weeds down and water if it gets too dry, they'd probably appreciate a bit of shade later in the summer as well since you're in a pretty hot zone. Peonies are fairly xeric plants, don't need or want a ton of water and they'll die if they're in a boggy area. You can use a bulb fertilizer on them late summer after they've stopped flowering or in the fall when you cut them back and again as you first start seeing growth in the spring. Isn't absolutely necessary but you will get bigger blooms, in my experience.

They look like are planted too deep for your location. If they do not bloom consider washing away some of the soil covering them in the fall.

The stems look like peonies. The leaves look like peonies. The buds look like peonies. I think you have peonies!

Others have said it before, but for the first spring/summer in a new home, wait to see what comes up! It's great that you have peonies that are in blooming condition already.

I can't explain why they are growing so far apart, other than possibly the owner divided them and spread them out so that over time, he would have more covering the area. It certainly looks like they were planted all at about a same distance apart, suggesting that it was done manually.

So my DB was mowing the yard yesterday and accidentally mowed them down... >_<

Any chance the roots have enough energy to put out some new leaves and survive until next year? Should I give them extra fertilizer or anything like that to help their chances?

Usually by the time they're as tall as yours they're done putting up new sprouts for the spring. There is certainly a chance they'll come back next year, though. I wouldn't fertilize now but some bulb fertilizer in the fall and then again when they first sprout next spring wouldn't hurt. Sorry they were mowed down, don't you hate when your plants are messed with? I need to get fishing line strung around my beds before the deer trample new growth...

Aww that's a bummer but thank you for the information. I'll just stay hopeful for next year! It would be nice to have something from the previous owners that's actually nice.

Definitely peonies - Congrats! And my husband has mowed over ours & our dogs have ran through the garden before, but they have come back so you should be okay and have blooms next year! Good luck!