Mathematics>Year 9>Unit 2

Non-Linear Relationships

Move beyond straight lines: transform and sketch parabolas, explore circles, hyperbolas and exponential graphs, and solve quadratic equations.

20 Lessons4 Checkpoints1 Unit QuizStage 5 Core
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Syllabus Outcomes

MA5-NLI-C-01

Graphs and interprets non-linear relationships.

Block A, Transformations of the Parabola
01

From Linear to Non-Linear

 02

The Basic Parabola y = x²

 03

Dilations: y = ax²

 04

Reflections: y = -x² and y = -ax²

 05

Vertical Translations: y = x² + c

 06

Combining: y = ax² + c

 07

Horizontal Translations: y = (x-h)²

Checkpoint 1, Transformations of the Parabola

Covers Lessons 1–7
Block B, Parabola Features & Sketching
08

Vertex and Axis of Symmetry

 09

x-Intercepts and y-Intercept of Parabolas

 10

Sketching and Identifying Parabolas

 11

The General Form y = a(x-h)² + k

Checkpoint 2, Parabola Features & Sketching

Covers Lessons 8–11
Block C, Other Non-Linear Graphs
12

Circles x² + y² = r²

 13

The Hyperbola y = k/x

 14

Exponential Relationships y = aˣ

 15

Comparing Non-Linear Graphs

 16

Graphing Non-Linear Relationships

 17

Applications of Non-Linear Relationships

Checkpoint 3, Other Non-Linear Graphs

Covers Lessons 12–17
Block D, Quadratic Equations & Synthesis
18

Introduction to Quadratic Equations

 19

Solving Quadratic Equations

 20

Unit Synthesis: Non-Linear Review

Checkpoint 4, Quadratic Equations & Synthesis

Covers Lessons 18–20

Unit Quiz

Full unit assessment