To find the slope of a parabola at a point you have to find is the first derivative of the function. This first derivative is the slope of the tangent of the parabola at the given point and it is the same slope of the parabola.
If you have the parabola with the general form y = Ax^2 + Bx + C
The slope at point (m,n) is:
y' = 2Ax + B
x = n
=> y ' = 2A(n) + B.
For example, find the slope of the parabole y = 3x^2 + 2x + 1, at x = 1
y' = 6x + 2
x = 1 => y' = 6(1) + 2 = 8.
So the slope at x = 1 is 8.
