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Suppose we have a prarbola $y^2 = 2px$ ....this is in fact $y = \sqrt{2px}$, so we plot it like a square root function, so it has no applied values for less than zero. However I saw in my textbook such a plot that for $y>0$ it looks like square root function indeed, and for $y<0$ it looks $y^2 = 2px$ all over again, though it shouldn't be even defined there...how come?

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  • $\begingroup$ Graph of $y^2=2px$ will obviously look like that of $y^2=2px$. Could you clarify what you mean to say ? $\endgroup$
    – Debashish
    Jun 23, 2014 at 9:54
  • $\begingroup$ square func are not defined so that they give out y<0 , hence the question $\endgroup$
    – Bak1139
    Jun 23, 2014 at 9:56
  • $\begingroup$ @Bak1139 It's not defined for $x < 0$. $y^2 = 2px$ is the same as $x = y^2 / 2p$, which is defined for all $y$. $\endgroup$
    – M. Vinay
    Jun 23, 2014 at 9:58
  • $\begingroup$ Graph of $y^2=2px$ will have positive as well as negative values of $y$ whereas the graph of $y=\sqrt{2px}$ will have only positive values of $y$ because $\sqrt{2px}$ means the positive square root of $2px$ $\endgroup$
    – Debashish
    Jun 23, 2014 at 10:00
  • $\begingroup$ @M.Vinay how would a sqaure of a positive number would give a negative one than? $\endgroup$
    – Bak1139
    Jun 23, 2014 at 10:00

1 Answer 1

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$y²=2px$ is not an equation of a function, it's the equation of a parabola! It's as simple as that, in fact its graph is the union of two function graphs $f$ and $g$:

$f(x)=\sqrt{2px}$

and

$g(x)=-\sqrt{2px}$

I hope you got your answer :)

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