I'm following a tutorial which says this:
Convert the following equation to a pair of parametric equations for $x$ and $y$ in terms of $t$: $$y=x^2+3$$ Step 1 - Set $t$ equal to $x^2$: $$t=x^2$$ Step 2 - Solve for x: $$x=\sqrt t$$ Step 3 - Substitute $t$ for $x^2$ in $y=x^2+3$: $$y=t+3$$
In step 2, I was thinking it should actually be $x=\pm\sqrt t$ instead of $x=\sqrt t$. Is that correct, if the domain of $y=x^2+3$ is all real numbers?
Unless it is explicitly claimed that $x \geq 0$ or $x < 0$ (exclusive), there is no much you can do other than considering each case separately.
Otherwise, as previously mentioned in the comments, it is more interesting to consider the parametrization $x = t$ and $y = t^{2} + 3$.
Hopefully this helps !