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

[SpaceKidd_N7]

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!

 

[LS1088]

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

 

[Simon Bridge]

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

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?

 

[SpaceKidd_N7]

Ohh okay, I totally get it now.

Thank you very much!

 

[Mark44]

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

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.