# Parabola constructed graphically from 3 points using slopes

- Author:
- smichr_1

- Topic:
- Parabola

A special quality of the parabola is that the slope between any two points

*is*the slope on the curve at half the horizontal distance between those two points. This property is used to geometrically make a graph of slope vs x and find the intersection of that line with a line parallel to the x-axis (where the slope would be zero). The vertical line through that intersection is the axis of symmetry for the parabola. With that axis, two of the 3 given points can be used to locate the focus (N), directrix (horizontal line through D) and vertex (T) of the parabola.