Answer
Please see the graph.
Work Step by Step
$y > (x-1)^2 -3$
$y=(x-1)^2-3$
$y=(x-1)(x-1)-3$
$y=x*x+x*-1+x*-1+(-1)(-1)-3$
$y=x^2-2x+1-3$
$y=x^2-2x-2$
$a=1$, $b=-2$, $c=2$
$x=-b/2a$
$x=-(-2)/2(1)$
$x=2/2$
$x=1$
The axis of symmetry (and the vertex) of the graph is at $x=1$.
We pick the point $(1,10)$ to see what side of the line to shade.
$y > (x-1)^2 -3$
$10 > (1-1)^2 -3$
$10 > 0^2 -3$
$10 > 0-3$
$10 > -3$ (true, so we shade the side of the line with this point)
