# Thread: graphing an absolute quadratic fuction

1. ## graphing an absolute quadratic fuction

I'm quite confused by the function y = |x^2 - 1|

I understand that y = x^2 - 1 when x^2 - 1 > 0 etc

But how do you solve it?

You get x^2 - 1 > 0
x^2 > 1
x > + or - 1
but it should be x<-1 and x>1

Is there some sort of inequation sign change when one of the sides is square rooted? Thanks in advance

2. Originally Posted by freswood
I'm quite confused by the function y = |x^2 - 1|

I understand that y = x^2 - 1 when x^2 - 1 > 0 etc

But how do you solve it?

You get x^2 - 1 > 0
x^2 > 1
x^2>1 means that |x|>1, or that x<-1, or x>1.

The first of these is because for negative numbers the absolute value
increases as the number becomes more negative.

RonL

3. Ahh thankyou that makes sense. How would I set that out in an exam?

4. Originally Posted by freswood
I'm quite confused by the function y = |x^2 - 1|
I understand that y = x^2 - 1 when x^2 - 1 > 0 etc

But how do you solve it?
You get x^2 - 1 > 0
x^2 > 1
x > + or - 1
but it should be x<-1 and x>1
Is there some sort of inequation sign change when one of the sides is square rooted? Thanks in advance
hello,

I start here:

x^2-1 > 0. Factorize

(x+1)(x-1) > 0. > 0 means the product is positive. A product of 2 factors is positive if the factors have equal signs: (+) * (+) > 0 or (-) * (-) > 0. "+" means greater as zero, "-" means smaller as zero.

So your inequality becomes:
Code:
x+1 > 0 and x-1 > 0   or  x+1 < 0  and x+1 < 0
x > -1 and x > 1        or   x < -1  and x < -1
x > 1       or    x < -1
This method only works if you can factorize the term.

tschüss

EB