Posted by **Lori** on Saturday, March 29, 2008 at 3:34pm.

I don't know which is which

y=(x+9)^2-3

I know it is all real numbers, but i don't know if my answer should be

[-3,00)

or

(-9,00)

Can some one explain this?

- Algebra -
**Damon**, Saturday, March 29, 2008 at 4:09pm
I do not know what your question is asking for so will describe the function.

This parabola opens up (holds water) because y gets big positive as x gets big positive or negative.

The axis of symmetry, and therefore x location of the vertex, is when the quantity (x+9) is zero. That is when x is -9

For example if you go one space left and right of x = -9, you should get the same y

well if x = -9-1 = -10, then y = 1-3 = -2

and if x = -9 + 1 = -8, then y = 1-3 = -2 sure enough the same.

Now to find the vertex, we already know that (x+9) is zero at x = -9 so we need y there, but it is obviously 0-3 = -3

so the location of the vertex is (-9,-3)

- Algebra -
**Damon**, Saturday, March 29, 2008 at 4:12pm
Now about your "all real numbers" comment.

Yes, the domain of x is all real numbers, you can find a y for any old x.

However we can not find any y below the vertex at y = -3 because the whole parabola is above the vertex at (-9,-3)

Therefore the Range of y is y greater than or equal to -3

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