y = x2 - 2x - 3 is a parabola. Since the x2 is positive, it opens upward (concave-up). If you factor the right hand side, you get (x+1) (x-3) so that means that the
x-intercepts are at -1 and +3. The vertex is halfway between these of course
(at x = 1). That means the vertex is at x = 1 and y = 12 - 2(1) - 3 = -4.
So draw a parabola shape with the vertex at (1, -4) and x intercepts at -1 and +3.
Hope this helps,
Stephen La Rocque.