Te reo Māori terms
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Learning objective overview
Master Teaching Guide coverage for this objective.
Current NZC (2007)
- No direct alignment recorded
New NZC (2026)
NZC26-P4-ALG-ER-P-Y10-03
Resources
- CorbettMaths - Cubic GraphsQuestions PDF · Answers
Terminology
- factorised form
- x-intercept
- y-intercept
- root
- repeated root
- multiplicity
- end behaviour
- leading coefficient
- turning point
Task goals
- Foundation: Read off the x-intercepts and y-intercept from a given factorised cubic or quartic equation and plot them on a set of axes.
- Proficient: Sketch the full graph of a factorised higher-order polynomial, correctly showing whether the curve crosses or touches the x-axis at each root based on its multiplicity and determining end behaviour from the degree and leading coefficient's sign.
- Excellence: Given a sketch or description of a higher-order polynomial graph (intercepts, turning/touching points, and end behaviour), reconstruct its factorised equation, including cases with a repeated factor or a non-unit leading coefficient.
Where this fits
What leads into this objective, and where it goes next.
Before
Sketching a parabola from factorised form (a=1)
Solving Quadratic Equations by Factorising (Null Factor Law)
Solving quadratics
You are here
Graphing Higher-Order Polynomials from Factorised Form
Next
Year 10 is the last year of this phase — the curriculum lists nothing after this. No extension resources on the site yet.
For teachers
Need the fuller teaching notes for this objective? Open the Teacher guidance PDF.