Why $y^2\ge x^4$ can be written as $|y|\ge x^2$?

Question

I'm studying the domain of $f(x,y)=\sqrt{y^2-x^4}$

Answer 1

As $y^2 \geq 0$ and $x^{4} \geq 0$, we may write $$\sqrt{y^2} \geq \sqrt{x^4},$$ which indicates that
$$\lvert y\rvert \geq x^{2}$$

Answer 2

Note that $$ y^2\geq x^4 \iff 0\leq y^2 - x^4=(|y|-x^2)(|y|+x^2)\iff|y|\geq x^2. $$