Answer
Please see the graph.
Work Step by Step
Three points on the curve:
$y=-x^2-2$
Line of symmetry:
$x=-b/2a$
$x=-0/2*-1$
$x=0$
$y=-x^2-2$
$y=-0^2-2$
$y=0-2$
$y=-2$
$(0,-2)$
Let $x=1$:
$y=-x^2-2$
$y=-1^2-2$
$y=-1-2$
$y=-3$
$(1,-3)$
Since $(1,-3)$ is one unit from the axis of symmetry, we also know $(-1,-3)$ is also one unit from the axis of symmetry and on the curve.