Question

Can I find the equation of a quadratic function when only two of its points are known?

Answer 1

The answer is no.

Think about the quadratic. When we substitute the points, `x` and `y` are no longer the variables in the system of linear equations; they become the constants. `a`, `b`, and `c` now become the variables of the system.
`>y=ax^2+bx+c`

If we substitute 2 points, we have 2 equations and 3 unknowns. This is an underdetermine system of linear equations, so many quadratics will go through those 2 points.

In general, if we have a degree `n` polynomial, we require `n+1` points to determine the polynomial function.