SOLUTION: I am trying to help my son with his Algebra but I don't understand it either! The problem says to identify the range and domain of each parabola. There are 2 pages of them but I'm

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Question 37624: I am trying to help my son with his Algebra but I don't understand it either! The problem says to identify the range and domain of each parabola. There are 2 pages of them but I'm going to try and figure them out from these two problems: y=-x^2-3 and the other is y= 2x^2 +3 . From reading in the book I think the domain on both is all real numbers but on the range on the first would it be all real numbers less than or equal to -3. And on the second would it be R= all real numbers greater than or equal to 3. I'm very unsure of this!
Answer by junior403(76) (Show Source):
You can put this solution on YOUR website!
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