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Transformation + root of a quadratic.

  1. Sep 27, 2012 #1
    1. The problem statement, all variables and given/known data

    2sqrt (x^2-2), sqrt (4(x^2-2)), x^2.

    The first 2 formulas are the same thing. However I want to how I would explain the transformation of x^2 to either or of those. I have tried a myriad of things to try get x^2 to any of those other two graphs. A quick answer would be appreciated.

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 27, 2012 #2
    for a test a tomorrow. Only thing I dont really get quadratic + root + transformation.

    How would I write X^2-9 rooted then stretched horizontally by a factor of 4 and y by a factor of 2 then right 2 and down 1.

    I will understand the idea if someone just solves this for me.
     
  4. Sep 28, 2012 #3

    HallsofIvy

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    I) Subtract 2 from y= x^2. Since that is a change in y, it moves the graph down two positions vertically.

    II) Multiply that by 4. That "stretches" the graph vertically, by a factor of 4.

    III) Take the square root. That will be a much more complicted change graphically, "stretching" vertically as long as 4(x^2- 2)< 1, "contracting" if 4(x^2- 2)> 1, with the amount of "stretch" or "contraction" depending upon x.
     
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