#### Answer

$y=1-\sqrt {-x}$

#### Work Step by Step

We start with $x + (y-1)^2=0$.
Subtract both sides by $x$.
$(y-1)^2=-x$
Take the negative square root of both sides, because we need to get the bottom half of the parabola.
$y-1=-\sqrt {-x}$.
Add 1 to both sides.
$y=1-\sqrt {-x}$.