3
$\begingroup$

Now, if I draw the following:
$3x+y=3$
$2x^2-y^2=-1$
With Wolfram I get the following graph.
enter image description here

But if I draw the following functions that I have solved for Y
$y=\sqrt{1+2x^2}$
$y=3-3x$
I seem to be loosing some information
enter image description here

Is all this simply a consequence of the following math:
$y^2=1+2x^2$
$y=\sqrt{1+2x^2}$

Squaring could cause this, but is that what I have done here? The reason for my post is that when doing the calculations by hand I still find the two intersections. But it is not visible in the graphs of the very same functions that on paper gives me what I want.

  • 7
    You're right. To complete things, plot the *negative* square root as well.2011-10-04
  • 1
    Note, for example, that $(0,-1)$ is on the graph of $y^2=1+2x^2$ but not on the graph of $y=\sqrt{1+2x^2}$. When you say you get both intersections by hand, surely that's because somewhere along the way you "square both sides" thereby re-introducing the other branch of the hyperbola.2011-10-04
  • 0
    Remember that $\sqrt{y^2} = |y|$, not $y$. So your first function should not be $y=\sqrt{1+2x^2}$, but rather $|y|=\sqrt{1+2x^2}$.2011-11-28

1 Answers 1