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Odd graph

  1. Mar 8, 2010 #1

    Mentallic

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    I came across this weird graph from another thread:

    [tex]y=\left(x^2-6x+8+\sqrt{x^4-12x^3+52x^2-96x+64}\right)^2[/tex]

    It seems that there is a root y=0 for the domain x=[2,4].
    I've never seen such weird behaviour on a graph before. How could analysis of this function (or not?) determine that there is a root for all values [itex]2\leq x\leq 4[/itex]?
     
  2. jcsd
  3. Mar 8, 2010 #2

    Redbelly98

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    That does seem weird, but I have figured out what is going on.

    The expression under the radical is the square of (x2-6x+8). So that expression (including the square root) is simply the absolute value of (x2-6x+8).

    They cancel whenever (x2-6x+8) is negative, which happens for 2<x<4.
     
  4. Mar 8, 2010 #3

    Mentallic

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    Nice one Redbelly :smile:
    I like this new little trick, it seems so nifty hehehe

    Thanks.
     
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