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

1 Answer
Aug 21, 2014

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.