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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
02 Your result
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FormulaValue = 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

Worked example

Inputs

X0
0 number
Y0
0 number
X1
1 number
Y1
1 number
X2
2 number
Y2
4 number
Evaluation position
1.5 number

Expected results

Value
2.25 number
Derivative
3 number

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter the labeled inputs using consistent units.
  2. Check the stated assumptions and calculate.
  3. 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.