THE FEUTEX TOOLKIT

Three-Node Polynomial Interpolation

Interpolate a quadratic through three data points and evaluate its value and derivative.

Math workspace● Runs in your browser

01 Your input

X0numberY0numberX1numberY1numberX2numberY2numberEvaluation positionnumber

02 Your result

View or copy raw result data

Result data

Formula

Value = y0*(x-x1)*(x-x2)/((x0-x1)*(x0-x2))+y1*(x-x0)*(x-x2)/((x1-x0)*(x1-x2))+y2*(x-x0)*(x-x1)/((x2-x0)*(x2-x1)); Derivative = y0*(2*x-x1-x2)/((x0-x1)*(x0-x2))+y1*(2*x-x0-x2)/((x1-x0)*(x1-x2))+y2*(2*x-x0-x1)/((x2-x0)*(x2-x1))

Sources and model references

https://mathworld.wolfram.com/LagrangeInterpolatingPolynomial.html

How to use this tool

Enter the labeled inputs using consistent units.
Check the stated assumptions and calculate.
Review each output and compare another input scenario.

Try this example

{
  "x0": 0,
  "y0": 0,
  "x1": 1,
  "y1": 1,
  "x2": 2,
  "y2": 4,
  "x": 1.5
}

Accuracy and scope

Quadratic interpolation, not a regression fit; extrapolation can be unstable. Finite floating-point arithmetic; results can lose precision near singular or extreme inputs.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.