Answer
Please see the graph.
Work Step by Step
$y=x^2+2x+3$
Let $x=-3$
$y=x^2+2x+3$
$y=(-3)^2+2*(-3)+3$
$y=9-6+3$
$y=3+3$
$y=6$
Let $x=-2$
$y=x^2+2x+3$
$y=(-2)^2+2*(-2)+3$
$y=4-4+3$
$y=0+3$
$y=3$
Let $x=-1$
$y=x^2+2x+3$
$y=(-1)^2+2*(-1)+3$
$y=1-2+3$
$y=-1+3$
$y=2$
Let $x=0$
$y=x^2+2x+3$
$y=(0)^2+2*(0)+3$
$y=0+0+3$
$y=3$
Let $x=1$
$y=x^2+2x+3$
$y=(1)^2+2*(1)+3$
$y=1+2+3$
$y=3+3$
$y=6$
We have the ordered pairs $(-3,6), (-2,3), (-1,2), (0,3), (1,6)$