If you Google African daisies you'll find lots of references to the annual Dimorphotheca. These African Daisies I bought are osteospermum. According to Osteospermums.com, the name comes from the Greek osteon (= bone) and Latin spermum (= seed). This member of the daisy family sometimes is called South African Daisy, Cape Daisy or Blue-eyed Daisy. The label on the plant might say annual, but they are half-hardy perennials, which means they won't survive multiple frosts but will survive if protected.
Give your African Daisies plenty of sun, water frequently and feed weekly with a general fertilizer of your choice. Be sure to deadhead to prolong flowering. If you need to prune for tidiness, go ahead. They will send up new shoots.