Slope of y=x^2-2x-3 at P (2,-3)

Recall that the derivative of this function, evaluated at x=2, is the slope of the tangent line to the graph of the function.

Thus, we begin by differentiating y=x^2-2x-3:

(dy/dx) = 2x - 2

Evaluated at x=2, (dy/dx) = (2) (2) - 2 = 4-2 = 2.

The slope of the tangent line to the graph of this function at (2, - 3) is 2.