Question 37624
You seem to be correct on both of these problems.
The domain of a parabola is all possible values for X.
In the case of vertical parabolas the domain is ALWAYS all real numbers.
The range of the parabola is all possible values for Y.
In the case of vertical parabolas this includes all real numbers in relation to its vertex.
So...
y=-x^2-3
when x=0, y=-3
this is the vertex of a parabola that opens down.
So the range is all real numbers less than or equal to -3.
And...
y=2x^2+3
when x=0, y=3
this is the vertex of a parabola that opens up.
So the range is all real numbers greater than or equal to 3.

Thanks for the question!
Alan