Description
Return completing-square shift and vertical offset.
Polynomial coefficients encode powers in a chosen order, with zeros, multiplicities and leading terms carrying different meanings. Local coefficient identities and necessary divisibility conditions can be checked without finding every root or proving a proposed factorization. Floating-point comparisons use the exact supplied values unless an explicit tolerance is provided.
Return completing-square shift and vertical offset.
When to use this tool
Use Quadratic Completing Square Offset when checking the stated coefficient, root-identity, index or divisibility term.
How to use the tool and how it works
- Enter a, b, c. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read shift, offset. Use the output convention below.
Return completing-square shift and vertical offset. Require a != 0; shift = b/(2*a), offset = c-b²/(4*a).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| a | A | Required. Finite number. |
| b | B | Required. Finite number. |
| c | C | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| shift | Positive b/(2*a) in a*(x+shift)^2+offset; vertex x is -shift. | Required. Finite number. |
| offset | Offset | Required. Finite number. |
{
"input": {
"a": 2,
"b": 8,
"c": 3
},
"output": {
"shift": 2,
"offset": -5
}
}Limitations and assumptions
- The rewritten form is a*(x+shift)²+offset, so vertex x is -shift; no symbolic derivation or numerical-error guarantee is produced.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use a complete symbolic or numerically appropriate polynomial method for root finding, full factorization and robust treatment of near-degenerate coefficients.
References
Similar or alternative tools
- Quadratic Discriminant Roundoff Scale
Return a magnitude scale for discriminant arithmetic.
- Binomial Square Cross Term
Return the binomial-square cross term.