How this calculation works
Substitute all three x-values into the recovered polynomial to verify the fit. Coincident x-values do not uniquely determine the coefficients.
Use divided differences to interpolate a polynomial of degree at most twoA worked example
(0,1), (1,4), (2,9) lie on x²+2x+1.
Good to know
If the points are collinear, the quadratic coefficient is zero.
Reference: OpenStax Algebra and Trigonometry (opens in a new tab) ↗
Read the result
Recover the coefficients of the polynomial through three points with distinct x-coordinates.
The primary result is labeled “Coefficient of x²”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
If the points are collinear, the quadratic coefficient is zero.
For a related exercise, try the quadratic equation solver.
A few questions, answered
How can I check the default inputs by hand?
(0,1), (1,4), (2,9) lie on x²+2x+1.
Which rule does this calculator apply?
Use divided differences to interpolate a polynomial of degree at most two