Hi, I don't really understand the graph of y^{2}=x^{2}. 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!
##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?
Or this ... If y^{2} = x^{2} then y^{2} - x^{2} = 0 so (y - x)(y + x) = 0 ∴ y = x or y = -x The graph of y^{2} = x^{2} looks like the union of the graphs of y = x and y = -x -- two straight lines.