Te reo Māori terms
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Learning objective overview
Master Teaching Guide coverage for this objective.
Current NZC (2007)
NA6-7
New NZC (2026)
NZC26-P4-ALG-ER-P-Y10-09
Resources
- CorbettMaths - Transformations of GraphsQuestions PDF · Answers
Terminology
- vertex form
- vertical translation
- horizontal translation
- reflection
- dilation
- y = a(x-h)^2+k
- narrower / wider than y = x^2
Task goals
- Foundation: Identify and sketch simple translations of y=x^2 given equations in vertex form with a=1, stating the shift left/right and up/down.
- Proficient: Identify and apply reflections (a<0) and dilations (|a|≠1) together with translations, matching a given equation to its transformed graph or vice versa.
- Excellence: Given a description of a combined sequence of transformations (or an unfamiliar transformed graph), derive the equation of the parabola and justify each transformation used, including working backwards from key features.
Where this fits
What leads into this objective, and where it goes next.
Before
Forming equations of given straight line graph (using y=mx+c)
Gradient
Linear Graphs from Algebraic Rules (Table of Values)
You are here
Transformations of the Parabola
Do
Determining the effect on graphs in the coordinate plane of changing the coefficient of x^2 and the fixed value c, for a range of quadratic equations of the form y = ax^2 or y = x^2 + c, where a is a positive integer and c is an integer
Statement▸
Year 10 · Algebra · Equations and relationships
NZC26-P4-ALG-ER-P-Y10-09
Next
Year 10 is the last year of this phase — the curriculum lists nothing after this. Extension resources: Drawing exponential graphs, Reading and forming parabolas in vertex form y = a(x - h)^2 + k where a is not 1.
Also under NA6-7:
For teachers
Need the fuller teaching notes for this objective? Open the Teacher guidance PDF.