The intercepts and the graph on your worksheet are not correct. Please see below for details:
[tex]x^2-2x-3=0[/tex] has solutions at x=-1 and x=3 (use the quadratic formula to solve). That means these are the x-intercepts, namely points:
(-1,0) and (3,0).
The y-intercept comes from setting x=0 and calculating the y value:
[tex]y=0^2-2\cdot0-3=-3[/tex]
so the y-intercept is (0,-3).
Now to the graph: Based on the form of the function we can see this is a quadratic function and its graph will be a parabola. You can reformat the expression in the following form
[tex]y = x^2-2x-3=(x-1)^2-4[/tex]
and that will indicate that the apex of the parabola (open up) will be at the point (1,-4).
Knowing the apex, the x intercepts, and the y intercept, we can graph it now.
Graph is in the image attached.
