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Stage 5 · Non-linear relationships C (Path) · Graph parabolas and describe their features and transformations · Topic: Non-linear relationships & functions · Year 9, 10

Graph quadratic relationships of the form y = (ax)² + bx + c by identifying and applying features of parabolas and their equations without graphing software

Dot point ID k-10-2022-stage-5-non-linear-relationships-c-path/nlc-par-stg5-05 · NESA code MA_K_10_CP_NLC_PAR_STG5_05 · See it on the NSW Curriculum website ↗

↩SupportBuild the prerequisite skills first · 7 resources ★EnrichExtension & rich tasks · 1 resource

Outcomes for this focus area (MA5-NLI-P-01)

MA5-NLI-P-01 interprets and compares non-linear relationships and their transformations, both algebraically and graphically (Path: Adv)

Core resources for this dot point

On-level resources, grouped by type. Need the building blocks? Use Support. Ready for more? Use Enrich.

Interactive tool

Interactive toolStarter Enrichment
Desmos Graphing Calculator
Desmos · Interactive (browser) · Free · Link checked 2026-10-15 · No prep
Use it for: Graph lines, parabolas and exponentials live; find intersections to solve simultaneous equations.
Also tagged to: Examine the gradient of the tangent to the curve y = a^x at …; Use graphing applications to identify the graphs of y = a^x …; Examine the gradient function of y = a^x with graphing appli…; Establish using graphing applications that replacing x by - … and 82 more
Interactive toolEnrichment
GeoGebra Classic
GeoGebra · Interactive (browser) · Free · Link checked 2026-10-15 · No prep
Use it for: Dynamic geometry and graphing for constructions and proofs.
Also tagged to: Examine the gradient of the tangent to the curve y = a^x at …; Use graphing applications to identify the graphs of y = a^x …; Examine the gradient function of y = a^x with graphing appli…; Establish using graphing applications that replacing x by - … and 84 more
Interactive toolStarter
Maths Is Fun: Graphing quadratic equations
Maths Is Fun · Interactive (browser) · Free · Link checked 2026-10-15 · No prep
Use it for: How to sketch parabolas from intercepts and vertex.
Also tagged to: Find x- and y-intercepts algebraically, where appropriate, f…

Video

VideoStarter
Corbettmaths video: Quadratic graphs: sketching using key points
Corbettmaths · Video · Free · Link checked 2026-10-15 · No prep
Use it for: Short worked-example video on quadratic graphs: sketching using key points to model the method before practice or for flipped revision.

Focus area resources

Checked resources for Non-linear relationships C (Path) as a whole (not mapped to a single dot point).

Unit/Planning
Stage 5 Unit 11 – applying exponentials (sample unit of learning)
NSW Department of Education · Sample unit (DOCX) · Editable document · Free · Link checked 2026-10-15 · Australian context, Editable, Teacher notes
Outcome codes found in document: MA5-FIN-C-02, MA5-NLI-C-01, MA5-NLI-C-02, MA5-NLI-P-01
Unit/Planning
Stage 5 Unit 12 – investigating parabolas (sample unit of learning)
NSW Department of Education · Sample unit (DOCX) · Editable document · Free · Link checked 2026-10-15 · Australian context, Editable, Teacher notes
Outcome codes found in document: MA5-ALG-C-01, MA5-ALG-P-01, MA5-ALG-P-02, MA5-EQU-P-01, MA5-EQU-P-02, MA5-NLI-C-01, MA5-NLI-C-02, MA5-NLI-P-01
Unit/Planning
Stage 5 Unit 9 – surveying (sample unit of learning)
NSW Department of Education · Sample unit (DOCX) · Editable document · Free · Link checked 2026-10-15 · Australian context, Editable, Teacher notes
Outcome codes found in document: MA5-GEO-C-01, MA5-NLI-P-01, MA5-TRG-C-02, MA5-TRG-P-01
Unit/Planning
Stage 5 Year 10 – maths in science elective (sample unit of learning)
NSW Department of Education · Sample unit (DOCX) · Editable document · Free · Link checked 2026-10-15 · Australian context, Editable, Teacher notes
Outcome codes found in document: MA5-LOG-P-01, MA5-NLI-P-01, MA5-RAT-P-01, MA5-RAT-P-02