# Thread: Finding domain and range

1. ## Finding domain and range

The question:

Determine the range of y = x^2 - 4x - 5 by writing y in the form (x-a)^2 + b.

I did as they said, and got:

(x-2)^2 - 9

But I don't understand why we would want to do this. Using the original equation, I can see that its a parabola, and graph it using the roots. Then the range is as simple as looking at it.

So how does this form help me? My first instinct is to expand it again, which defeats the purpose. Any ideas? Thanks.

Edit: I just noticed that the variable 'b' is the minimum point of the curve. Is this a co-incidence?

2. If the minimum point is $\displaystyle y = -9$, then what do you think the range of the function is?

3. Originally Posted by Glitch
The question:
Determine the range of y = x^2 - 4x - 5 by writing y in the form (x-a)^2 + b.
and gotx-2)^2 - 9
But I don't understand why we would want to do this.
$\displaystyle (x-2)^2\ge0$ so $\displaystyle (x-2)^2-9\ge-9$.
It is easy to see the range?

4. Originally Posted by Glitch
The question:

Determine the range of y = x^2 - 4x - 5 by writing y in the form (x-a)^2 + b.

I did as they said, and got:

(x-2)^2 - 9

But I don't understand why we would want to do this. Using the original equation, I can see that its a parabola, and graph it using the roots. Then the range is as simple as looking at it.

So how does this form help me? My first instinct is to expand it again, which defeats the purpose. Any ideas? Thanks.

Edit: I just noticed that the variable 'b' is the minimum point of the curve. Is this a co-incidence?
By doing that, you know the minimum/maximum point of the graph where in this case it's a minimum.

5. Sorry, I should have made it clear. I know the answer, (which is [-9, inf) for anyone that's interested), but I don't know why they want me to answer it using the form (x-a)^2 + b.

Edit: Looks like you guys are too quick! Reading the other posts now.

6. Originally Posted by Plato
$\displaystyle (x-2)^2\ge0$ so $\displaystyle (x-2)^2-9\ge-9$.
It is easy to see the range?
That's really awesome! I didn't notice that at all! Thanks!