The graph of the function y=x^ - x - 2

What's the exponent of x?   Looks like you inadvertently left that out.

I'm assuming that you mean y = x^2 - x - 2.

This is a quadratic function, and its graph is that of a parabola.

Important points on this parabola are as follows:

x-intercepts, y-intercepts, vertex

Finding these four points will enable you to graph this function nicely.

How do you find the x-intercepts?  Set the function = to 0 and solve for x:
x^2 -x -2 = 0 = (x-2)(x+1) = 0, so x = {2,-1}.  The y-values are both 0.  The intercepts are (2,0) and (-1,0).

How do you find the y-intercept?  Let x=0 and find y:  y = 0^2 - 0 -2 = -2, so the y-intercept is (0,-2). 

Finally, how do you find the vertex?  One way would be to find x = -b/(2a),
where a, b and c are the coefficients of a quadratic.  Here, a=1, b= -1 and c=-2.

Then x = -(-1) / [2(1)] = 1/2.  The x-coordinate of the vertex is 1/2.  Subst. this into the original equztion to determine the y-coordinate of the vertex.

Graph all 4 points and then sketch the graph of this parabola.