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

  • #1

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!
 

Answers and Replies

  • #2
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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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  • #3
Simon Bridge
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##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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  • #4
Ohh okay, I totally get it now.

Thank you very much!!
 
  • #5
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##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.
 
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