Finding the Rule for Quadratic Number Patterns

Find the rule y = ax^2 + bx + c from a table using first and second differences, then check the rule.

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Learning objective overview

Master Teaching Guide coverage for this objective.

Current NZC (2007)
  • NA5-9
New NZC (2026)
  • NZC26-P4-ALG-ER-P-Y9-11
  • NZC26-P3-ALG-ER-P-Y8-06

Resources

Terminology

  • Quadratic sequence
  • Table of values
  • First difference
  • Second difference
  • Coefficient
  • Rule
  • Check by substitution

Task goals

  • Foundation: Complete first and second differences and use second difference = 2a to find a.
  • Proficient: Use the first first-difference = 3a + b and the first term = a + b + c to find the complete rule y = ax^2 + bx + c.
  • Excellence: Derive the three shortcuts, handle negative coefficients or a missing table entry, and verify a rule against another term.

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Finding the Rule for Quadratic Number Patterns

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