Te reo Māori terms
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Learning objective overview
Master Teaching Guide coverage for this objective.
Current NZC (2007)
NA5-9
New NZC (2026)
NZC26-P4-ALG-ER-P-Y10-03
Resources
- CorbettMaths on drawing a parabolaQuestions PDF · Answers
- Dr Austin Maths - Sketching Quadratic Graphs Practice GridQuestions PDF · Answers
Terminology
- factorised form
- x-intercept
- root
- axis of symmetry
- vertex
- turning point
- y-intercept
Task goals
- Read the two x-intercepts (roots) directly from a parabola given in factorised form y = (x - p)(x - q), including the repeated-root case y = (x - p)^2.
- Find the axis of symmetry of a factorised-form parabola as the midpoint of its two roots, x = (p + q) / 2.
- Find the coordinates of the vertex (turning point) by substituting the axis-of-symmetry x-value back into the equation.
- Find the y-intercept of a factorised-form parabola by substituting x = 0.
- Write a parabola's equation in factorised form given its roots, including a repeated root, and given the axis of symmetry plus one root.
- Explain why the axis of symmetry sits halfway between the roots, and identify or correct a student's sign or axis-of-symmetry error made when reading factorised form.
- Expand a factorised-form equation and compare factorised form with vertex form, describing an advantage or limitation of each.
Where this fits
What leads into this objective, and where it goes next.
Before
Completing the Square
Using algebra to find the point of intersection of two lines
Algebra with geometry
You are here
Sketching a parabola from factorised form (a=1)
Do
Solving quadratic equations that are factorised or of the form x^2 + c = 0 (where c is an integer), and connecting the solutions to the x-intercepts of the related graph
Statement▸
Year 10 · Algebra · Equations and relationships
NZC26-P4-ALG-ER-P-Y10-03
Also under NA5-9:
For teachers
Need the fuller teaching notes for this objective? Open the Teacher guidance PDF.