determine the domain and range of f(x)=-2x squared + 6x+3

the "domain" is all legal x values
are there any x values that would produce undefined results?

the "range" is the set of all values f(x) will take on when you sweep x across the entire domain
does f(x) have a minimum or maximum value?

just to add. Whenever there is no denominator or square root in the question x can be any value. So domain = xER