Quadratic Polynomial Generator, Interpolator and Plotter

This script generates a quadratic polynomial from three points. The x coordinates x1 through x4 must all be different. The script will also interpolate (or even extrapolate!) to give a y value for any x coordinate, x5. Just for the sake of example, the page automatically loads width the results from the three points (-1,-1), (2,2) and (3,1) with an interpolation to x=2.5.

x1
y1
x2
y2
x3
y3
x4

y=1+1.5x
-0.5x2

y(x4)=1.625

or

y=1+1.5*x
-0.5*x**2