How do you find the vertex of a parabola with two points?
There are infinite number of parabolas passing through two given points. Therefore, this problem has no solution.
The logic behind this is simple. Generally speaking, parabola is determined by a quadratic polynomial
There are three unknown coefficients here:
To determine three unknown variables we need three equations. That's why we need three given points
Solving this system of three linear equations with three unknown variable produces coefficients