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

## Main Question or Discussion Point

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!

third quadrant - x < 0 and y < 0;
for some value a, x = -a and y = -a;
x^2 = y^2 = a^2

• 1 person
Simon Bridge
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?

• 1 person
Ohh okay, I totally get it now.

Thank you very much!!

Mark44
Mentor
##y^2=x^2\Rightarrow y=\pm\sqrt{x^2}##

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

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