The basil plants I started from the cuttings and roots of a bagged basil plant are thriving. The picture below shows the ones I started from the roots. This was two weeks ago, when I'd already pinched them back a few times so I could use home-grown basil in recipes. Pinch or cut basil stems just above a young pair of leaves to encourage the plant to form two new stems. You'll also slow down the flowering, which tends to make the basil bitter.
It's time to think about planting for fall crops. Remember that