Lets say I have a parabola of the following form:
$$ y = ax^2 + bx + c, \tag{1} $$
where, $a\ne 0, b\ne 0, c\ne 0$. Now, how the following graph should look like?
$$ \sqrt{y} = \sqrt{ax^2 + bx + c}. $$
I understand that in a specific case(not related to ours), if $y = x^2, $ then $\sqrt{y}$ is no longer a parabola. However, I have tried to graph a parabola of the form (1) and then took the square root. The result looked like another parabola except it was not as smooth as the original. Is there anything general we can say about taking the square root of a parabola?