What is the equation of this curve? (see details)
If you have two points (a,b) and (c,d), there are an infinite number of parabolas that can go through these points. If you plot all of the vertices of these parabolas, they create a curve. What is the formula for this curve?
Here is an image showing multiple parabolas through two points.
This is NOT homework.
This question is in the General Section. Responses must be helpful and on-topic.