The word "care" can be tricky to use because of the specific combinations it occurs in. It can mean "starosti", like worries, especially in songs. It can mean "starostlivosť" in expressions like "health care", "child care" or "care center". Then there are the expressions for "starať sa o ...": first of all "take care of", similar to "look after" but often focusing on someone who is sick, and then "care for", say an elderly relative.

"Take care of" can also mean "vybaviť", as in "I'll take care of the tickets," and "care for" can also mean "mať rád", like "Thanks, but I don't care for spinach." Be careful ;-) with "care about", because this means "(ne)záleží (mi)", as in "people who care about others", or even "je mi to jedno", like "I don't care if your brother's seven feet tall."