Graphs interpretation question

Question

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?

Answer 1

$y²=2px$ 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 :)