Don't understand the graph of y^2=x^2

  1. Hi,

    I don't really understand the graph of y2=x2. When I plot it in wolfram alpha, I get a plot that looks like an x or two diagonal intersecting lines that go through the origin. I can understand why there are points in the first, second, and fourth quadrants, but I am confused as to why there are points in the third quadrant.

    This isn't for any homework, I'm just trying to study for an exam.

    Thanks a lot!
  2. jcsd
  3. third quadrant - x < 0 and y < 0;
    for some value a, x = -a and y = -a;
    x^2 = y^2 = a^2
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  4. Simon Bridge

    Simon Bridge 15,299
    Science Advisor
    Homework Helper
    Gold Member

    ##y^2=x^2\Rightarrow y=\pm\sqrt{x^2}##

    if ##y=+\sqrt{x^2} = |x|##

    then ##y=-\sqrt{x^2}=\cdots##

    So what do you get if you plot both on the same axis?
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  5. Ohh okay, I totally get it now.

    Thank you very much!!
  6. Mark44

    Staff: Mentor

    Or this ...
    If y2 = x2
    then y2 - x2 = 0
    so (y - x)(y + x) = 0
    ∴ y = x or y = -x

    The graph of y2 = x2 looks like the union of the graphs of y = x and y = -x -- two straight lines.
    1 person likes this.
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