Here is the sqrt function with only one call to Sqrt:

sqrt[x_] := Module[{sq = Sqrt[x]}, {sq, -sq}]

It's about the same speed as two calls to Sqrt.

But my real point was that if you want different behaviour from a function, go ahead and modify it to suit your needs.

This would become hopelessly complicated:

2==Sqrt[4]
True

now returns True. But if it would return {-2,2}, it would stay unevaluated:

2=={-2,2}

Of course you could change the definition of Equal, to check if ONE of them is correct... but then you get into trouble if you want to check 2 things at the same time:

{2,3} == {1,2}+1

So in the end this is not a good idea ;) A similar problem occurs for trigonometric functions. For example the ArcCos (or ArcSin ArcTan..) returns and angle, but it can just as well return the angle + 2Pi. So you have to make a choice, because there are infinite! In the complex plane this becomes even more complex, and one has to choose a so-called branch cut and decide very carefully which answer should be returned.

There is an entire page about it HERE

Hmm, interesting... :)

Though, of course, it's still using two Sqrt functions. But, still another interesting approach to it. ;)

Thx, Eric!

So, long and short of it, plot both halves, 'cause there's no other solution? Got it.

Would still prefer there was some way to plot the reflection of the parabola with a single function, rather than 2 half-functions. Ahh well, guess you can't always get what you want, eh? ;)

The square root function is just that: a function. By convention, it returns the positive square root.

When I was young, you could find books referring to multi-valued functions, so you would get ± in the results. This was also a convention, but had to be resolved once computers came to be used, since they only 'like' single valued functions, which are the only ones that are, by definition, functions anymore.

You might still be able to find these books, but they need to be treated as historical artifacts.

So, you need to use a plot of two functions (+sqrt[x] and -sqrt[x]), or either of the solutions provided by other responders.

Once you get your head around that, try plotting the cube root of x. Then you can learn about principal values. ;-)

You could use ParametricPlot.

Clear[x, y, t]
x[t_] := t^2;
y[t_] := t;
ParametricPlot[{x[t], y[t]}, {t, -7, 7}]