You usually ‘take care of something or someone’. In this case, you look after a person or thing.
It’s your duty to take care of your old parents.
When you tell someone to ‘take care’, what you mean is that you want the person to be careful.
Tell the children to take care when they cross the busy road.
Nowadays, lots of people use the expression ‘take care’ to mean goodbye. It is mostly used in informal contexts.
Look at the time! I’ve got to get going. You take care.
Source: “The Hindu” – Know Your English Column – Dec. 25, 2007