# Thread: An expression representing the following function...

1. ## An expression representing the following function...

So I'm stuck on this question: find an expression for the function whose graph is the bottom half of the parabola, $x+(y-3)^2=0$. It should be expressed in terms of x according to the text that I'm working from.

The problem I'm having is actually isolating y without encountering a negative square root...Now, I haven't learned how to deal with complex numbers much so I'm not sure if that's the only way to do this. If it's possible to do this normally, could I have some hints?

2. If you're expressing it in terms of $x$ then

$x = -(y - 3)^2$.

3. Oops, I meant expressing it as y in terms of x so that's it's $y=$

4. $(y - 3)^2 = -x$

$y - 3 = \pm \sqrt{-x}$

$y = 3 \pm \sqrt{-x}$.

If you want the lower half then only accept

$y = 3 - \sqrt{-x}$.

5. Oh, is that really an acceptable answer? I got that but I wasn't sure if it was right due to the negative radicand...I guess I got thrown off by all the teachers always saying it's a big no-no. Thanks a lot.

6. Is $-x$ always a negative number?

7. I know it isn't when it's either 0 or a negative number but I was only thinking about the notation so I didn't really concern myself with anything else...Plus, the question didn't really allow us to write a domain.

8. Originally Posted by VectorRun
I know it isn't when it's either 0 or a negative number but I was only thinking about the notation so I didn't really concern myself with anything else...Plus, the question didn't really allow us to write a domain.
Doesn't matter, there's such a thing as an implied domain. There's nothing wrong with the notation as long as it's possible for any value of $x$.