Math / CALCULATOR

Composition of Two Quadratic Functions

Composition of Two Quadratic Functions with a worked example and explicitly bounded inputs.

Runs on your deviceUpdates as you typeFormula & example ↓
01

Your inputs

Adjust the values to explore a different result.

Enter f quadratic coefficient.
Enter f linear coefficient.
Enter f constant.
Enter g quadratic coefficient.
Enter g linear coefficient.
Enter g constant.
Enter x.

Formula

g(x)=Ax²+Bx+C; f(g(x))=a g(x)²+b g(x)+c.
  • Use the units shown beside each field.
  • Results update automatically whenever you change an input.
  • Displayed values use up to four decimal places, or scientific notation for very small or large numbers. Calculations use standard floating-point arithmetic; exact integer and fraction tools identify their own precision rules.
  • Numerical evaluation of two quadratics (including linear/constant cases); not arbitrary expression parsing.

Example Calculation

Example inputs
  • f quadratic coefficient: 1
  • f linear coefficient: 0
  • f constant: 1
  • g quadratic coefficient: 0
  • g linear coefficient: 2
  • g constant: 0
  • x: 3

f quadratic coefficient = 1; f linear coefficient = 0; f constant = 1; g quadratic coefficient = 0; g linear coefficient = 2; g constant = 0; x = 3. Primary result: 37.

Frequently asked questions

How do I use this calculator?

Enter f quadratic coefficient, f linear coefficient, f constant, g quadratic coefficient, g linear coefficient, g constant, x. The result updates automatically. Use Reset to restore the example values.

What method does it use?

g(x)=Ax²+Bx+C; f(g(x))=a g(x)²+b g(x)+c.. Numerical evaluation of two quadratics (including linear/constant cases); not arbitrary expression parsing.

Why might a rounded result differ?

The calculation keeps full numeric precision internally, then rounds the displayed result. Rounding intermediate steps by hand can produce a slightly different answer.

Are my inputs saved online?

No. This calculator processes your inputs in your browser. A recently used list stores only calculator names on this device, not your entered values.

Check the assumptions and units before using this result. Read about calculation methods.