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THE FEUTEX TOOLKIT

Two-Variable Quadratic Stationary Point

Find the stationary point and minimum value of a positive-definite quadratic form.

Math workspace● Runs in your browser
01 Your input
02 Your result
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FormulaX = (b*e-c*d)/(2*(a*c-b**2)); Y = (b*d-a*e)/(2*(a*c-b**2)); Minimum = f-(c*d**2-2*b*d*e+a*e**2)/(4*(a*c-b**2))
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Made for real tasks

  • Find the stationary point and minimum value of a positive-definite quadratic form.
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Worked example

Inputs

x² coefficient
2 number
xy half-coefficient
1 number
y² coefficient
3 number
x linear coefficient
-4 number
y linear coefficient
-6 number
Constant
10 number

Expected results

X
0.6 number
Y
0.8 number
Minimum
6.4 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 x² coefficient, xy half-coefficient, y² coefficient, x linear coefficient, y linear coefficient, constant.
  2. Use the displayed units and confirm the model assumptions.
  3. Calculate and compare the outputs against your input scenario.

Try this example

{
  "a": 2,
  "b": 1,
  "c": 3,
  "d": -4,
  "e": -6,
  "f": 10
}

Accuracy and scope

Convention a*x²+2*b*x*y+c*y²+d*x+e*y+f. Unconstrained minimum only.

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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.