Te reo Māori terms
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Learning objective overview
Master Teaching Guide coverage for this objective.
Current NZC (2007)
NA6-5
New NZC (2026)
NZC26-P4-ALG-ER-K-Y10-02NZC26-P4-ALG-ER-K-Y10-04NZC26-P4-ALG-ER-P-Y10-09
Resources
- No external resource is currently specified.
Terminology
- Discriminant
- Real distinct roots
- Repeated root
- No real roots
- x-intercepts
Task goals
- Foundation: Calculate the discriminant $b^2-4ac$ for a given quadratic and state whether it is positive, negative, or zero.
- Proficient: Use the sign of the discriminant to classify the roots as two real distinct roots, one repeated real root, or no real roots, and relate this to the number of x-intercepts on the parabola.
- Excellence: Find the value(s) of an unknown coefficient or constant so that a quadratic has a specified nature of roots (e.g. equal roots or no real roots), justifying the answer using the discriminant.
Where this fits
What leads into this objective, and where it goes next.
Before
Solving Quadratic Equations by Factorising (Null Factor Law)
Solving quadratics
Solving Irrational (Square-Root) Equations
You are here
Determining the Nature of the Roots of a Quadratic (Discriminant)
Know
Any positive real number has two square roots: one positive (the principal square root) and one negative (e.g. for 16, 4 and −4).
Statement▸
Year 10 · Algebra · Equations and relationships
NZC26-P4-ALG-ER-K-Y10-02
Know
There are 0, 1, or 2 real-number solutions to x^2 = a, where a is a number.
Statement▸
Year 10 · Algebra · Equations and relationships
NZC26-P4-ALG-ER-K-Y10-04
Also under NA6-5:
For teachers
Need the fuller teaching notes for this objective? Open the Teacher guidance PDF.