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
- vertical scale factor
- coefficient a
- narrower / wider than y = x^2
- stretch
- compression
- y = ax^2
- y = a(x-h)^2+k
Task goals
- Foundation: Sketch and compare y = x^2 with y = ax^2 for simple positive integer values of a, describing the parabola as narrower or wider.
- Proficient: Determine the vertical scale factor a from a graph or table of values, including cases where 0 < a < 1 or a is negative, and write the corresponding equation.
- Excellence: Combine a vertical scale factor with translations (y = a(x-h)^2+k) to sketch or reconstruct a full parabola equation from a labelled graph, and justify the effect of a algebraically.
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
Parabolas: Vertical Scale Factor
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.