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Math Help - graphing an absolute quadratic fuction

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by freswood View Post
    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
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  3. #3
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    Ahh thankyou that makes sense. How would I set that out in an exam?
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  4. #4
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    Quote Originally Posted by freswood View Post
    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
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