Te reo Māori terms
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Learning objective overview
Master Teaching Guide coverage for this objective.
Current NZC (2007)
NA6-5NA6-7
New NZC (2026)
NZC26-P4-ALG-ER-P-Y10-09
Resources
- CorbettMaths - Turning Points Using Completing the SquareQuestions PDF · Answers
Terminology
- completed square form
- turning-point form
- completing the square
- vertex
- axis of symmetry
- maximum value
- minimum value
- y = a(x-h)^2+k
Task goals
- Foundation: Complete the square for monic quadratics (a=1) and state the resulting turning point coordinates.
- Proficient: Complete the square for non-monic quadratics (a≠1) and sketch the parabola using the turning point, axis of symmetry, and direction of opening.
- Excellence: Use completed square form to solve graphical-model problems, including finding maximum/minimum values in context and deriving a parabola's equation from given transformational features.
Where this fits
What leads into this objective, and where it goes next.
Before
Linear Graphs from Algebraic Rules (Table of Values)
Comparing sequences: nth terms, graphs and intersection
Forming equations of given straight line graph (using y=mx+c)
You are here
Parabolas in Completed-Square (Turning-Point) Form
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.
For teachers
Need the fuller teaching notes for this objective? Open the Teacher guidance PDF.