I bought cut roses and after the flower head tipped there is new growth off of the stem How do I replant this?

The new growth is leafy matter coming from the stem in several spots. I have changed the water in the vase, but done nothing else to promote the growth. Everyday when I come home from work it is about a quarter of an inch longer than when I left in the morning. I would like to be able to plan this and ideally get a new rose bush.

I bought cut roses and after the flower head tipped there is new growth off of the stem How do I replant this?
Go buy some "root harmone" from walmart or any garden center...cut the stem below a node on the stem at an angle....wet it dip the stem in root hormone..shake ecxess off and plant in potting soil..within 2 weeks it will start roots in the soil..cost about 3.00