Parabolas from 3 Points
Why This Exists
I made this to demonstrate the fact that a parabola can be defined using 3 pieces of information. Normally these are coefficients (ax2 + bx + c) or the vertex and leading coefficient (a(x - h)2 + k). But, a parabola can also be defined by three points anywhere on a graph. It's a fun and tough puzzle for high-school level math.
I've wanted to make this for a long time, and I tired, but I only recently started thinking about the problem in the right way. I first solved a more simplified problem (step 2), then generalized it (step 1 & 3).
Method
- Move the points to a better position
- Find the quadratic that fits the new points
- Move the parabola back to the original points
Click the desmos logo to see a better explanation and the calculated values.