Greetings, welcome to the Forums.
Cordyline is a genus of monocot shrubs & trees, in the Lomandra family (Lomandraceae). Many cultivars with unusually coloured and variegated foliage have been bred and selected for ornament. The correct pronunciation of
Cordyline involves four syllables, with the final 'e' being pronounced as a long vowel.
The photo submitted by the OP shows a black and red-leaved form of Ti Plant (
Cordyline fruticosa, formerly
C. terminalis) in the far corner of the front bed. This may be the cultivar known as
C. fruticosa 'Florida Red'.
Cordyline fruticosa is native to parts of Queensland, New Guinea and Melanesia, but cultivars are grown worldwide in warm regions for the spectacular foliage. There are many photos online.
The photo in the third post shows a pink-leaved cultivar of
Cordyline australis (or a hybrid), native to New Zealand.
Cordyline australis is another very popular species in horticulture, due to its often arborescent stature, hardiness in temperate climes, and striking foliage.
The plant pictured may be the very popular cultivar
Cordyline x 'Sprilecpink', though there are other similar cultivars with pink and red leaves.
Cordyline x 'Sprilecpink' is purported to be a hybrid of
C. australis and
C. banksii, and is commonly sold under the trade name of
Cordyline Electric Pink™, Plant Patent #19213.
Pictured below is another partially pink-leaved cultivar:
Cordyline sellowiana 'Pink Joy' (species synonyms:
C. brasiliensis, C. glauca).
The species is native to tropical South America, but this cultivar is now grown worldwide, and has also received a Plant Patent #19959.
Despite it's tropical origins, I grow it very well outdoors in-ground in my USDA Zone 9b garden.
I've not grown Pink Cordyline myself but hopefully someone here will be able to help you out.
We are talking about this one, right:
