1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

  1. Oct 19, 2013 #1

    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. Oct 19, 2013 #2
    third quadrant - x < 0 and y < 0;
    for some value a, x = -a and y = -a;
    x^2 = y^2 = a^2
  4. Oct 19, 2013 #3

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper

    ##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?
  5. Oct 19, 2013 #4
    Ohh okay, I totally get it now.

    Thank you very much!!
  6. Oct 20, 2013 #5


    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook