Determine the domain and range of the function
f(x) = x^2 + 6x
I know the domain is all real numbers, but I am not sure how to find the range

Question

Determine the domain and range of the function
f(x) = x^2 + 6x
I know the domain is all real numbers, but I am not sure how to find the range

mertsj · Answer

This is a parabola.  It is concave upward.  Therefore the vertex is the low point.  Find the y coordinate of the vertex and the range will be all real numbers greater than or equal to that y value.

anonymous · Answer

Is there a formula that I use

anonymous · Answer

how do I find the y coordinate?

mertsj · Answer

x=-b/2a will give the x coordinate of the vertex.  Plug that back in to find the y coordinate of the vertex.

anonymous · Answer

I got 3 as the x coordinate, is that right?

mertsj · Answer

-6/2=-3 NOT 3

anonymous · Answer

oh okay, forgot the negative sign. So I plug back -3 into the equation?

mertsj · Answer

yes

anonymous · Answer

I got -9

mertsj · Answer

me too.

anonymous · Answer

so is that the range?

mertsj · Answer

Find the y coordinate of the vertex and the range will be all real numbers greater than or equal to that y value.

anonymous · Answer

Okay, so how do I find the y coordinate now?

anonymous · Answer

I thought -9 was the y coordinate

mertsj · Answer

Yes.  -9 is the y coordinate of the vertex.

mertsj · Answer

the range will be all real numbers greater than or equal to that y value.

anonymous · Answer

oh okay, thank you I got it!

mertsj · Answer

yw