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?