The word care is used both as a verb and as a noun in a similar manner to he verb and noun concern. Study the examples below, and pay close attention to the use of prepositions with 'care' in phrasal verbs.
Care: Noun -
1) What is done to provide and protect that which is necessary for the health or maintenance of something or someone.
2) Thoughts that concern you about something
Unfortunately, he has many cares at the moment. (1)
The care of my children is the most important factor in my life.(1)
She doesn't have a care in the world. (2)
Carol takes excellent care of her dog.
You need to take care of your toys if you want them to last.
Care is also used as a verb in the phrasal verbs to care for, and to care about.
To Care For
1) To do what is necessary to help and maintain a person or objet. The meaning of to care for is synonymous with to look after.
She cares for her mother who lives with her.
I care for a number of cats who drive me crazy!
2) To like or be fond of something.
I don't care for football.
What type of painters do you care for?
To Care About
To be concerned about something. Use the preposition 'about' when followed by an object.
She cares a lot about her children's future.
Do you care about this?
Do not use 'about' when used in a simple sentence in either the positive or the negative as a response to a statement:
What do you think about the election?
- I don't care.
Why aren't you working harder?! Don't you care?!
I care! It's very difficult.
Do not use 'about' when followed by a conjunction. This is same sense as a short sentence, but combined with another sentenced through the use of a conjunction.
She doesn't care, but I keep asking her to help.
I care, and I will help you.