What students learn in AC9M9A04
This unit helps students build a clear, usable understanding of And graph quadratic functions, solve quadratic equations graphically and numerically.... The goal is not to memorise one answer pattern. Students should be able to explain the idea, recognise it in a new example and apply it in a short practice or worksheet task.
- Start with the main idea: identify and graph quadratic functions, solve quadratic equations graphically and numerically, and solve monic quadratic equations with integer roots algebraically, using graphing software and digital tools as appropriate.
- Use concrete examples, pictures, oral explanation and short written responses before moving to independent practice.
- recognising that in a table of values, if the second difference between consecutive values of the dependent variable is constant, then it is a quadratic graphing quadratic functions using digital tools and comparing what is the same and what is different between these different functions and their respective graphs; interpreting features of the graphs such as symmetry, turning point, maximum and minimum values, and determining when values of the quadratic function lie within a given range
- Finish with mixed questions so students must choose the correct strategy rather than copy the last example.
Curriculum coverage and elaborations
The content description and elaborations below show the curriculum ideas taught in this unit. Items marked as teaching context support lesson planning but may not appear in the initial eight-question activity.
- Content description: identify and graph quadratic functions, solve quadratic equations graphically and numerically, and solve monic quadratic equations with integer roots algebraically, using graphing software and digital tools as appropriate
- E1: recognising that in a table of values, if the second difference between consecutive values of the dependent variable is constant, then it is a quadratic
- E2: graphing quadratic functions using digital tools and comparing what is the same and what is different between these different functions and their respective graphs; interpreting features of the graphs such as symmetry, turning point, maximum and minimum values, and determining when values of the quadratic function lie within a given range
- E3: solving quadratic equations algebraically and comparing these to graphical solutions
- E4: using graphs to determine the solutions of quadratic equations; recognising that the roots of a quadratic function correspond to the x-intercepts of its graph and that if the graph has no x-intercepts, then the corresponding equation has no real solutions
- E5: relating horizontal axis intercepts of the graph of a quadratic function to the factorised form of its rule using the null factor law; for example, the graph of the function y=x^2-5x+6 can be represented as y=(x-2)(x-3) with x-axis intercepts where either (x-2)=0 or (x-3)=0
- E6: recognising that the equation x^2=a, where a>0, has 2 solutions, x=\sqrt a and x=-\sqrt a; for example, if x^2=39 then x=\sqrt{39}=6.245 correct to 3 decimal places, or x=-\sqrt{39}=-6.245 correct to 3 decimal places, and representing these graphically
- E7: graphing percentages of illumination of moon phases in relation to First Nations Australians’ understandings that describe the different phases of the moon (teaching context)
How to use this unit
Read the topic guide, use the teacher slide for instruction, then complete the Worksheet, Practice and Test. These three activities use the same eight-question unit bank.
Teacher resource
AC9M9A04 teacher slide
Use this one-page PDF to introduce the key idea, vocabulary and teaching sequence before students begin the activities.
Open teacher slide (PDF)Common mistakes to watch for
- Rushing to a rule before checking the concrete model, drawing or number sentence.
- Using the correct answer once but not being able to explain why it works.
- Mixing up similar vocabulary such as more/less, before/after, longer/shorter or equal groups/sharing.
International curriculum mapping
This table gives closest-topic mapping for search and planning. The Australian Curriculum code is exact; overseas entries are broad equivalents because each jurisdiction structures outcomes differently.
| Region | Curriculum | Closest mapping |
|---|---|---|
| Australia | Australian Curriculum v9.0 | AC9M9A04 — identify and graph quadratic functions, solve quadratic equations graphically and numerically, and solve monic quadratic equations with integer roots algebraically, using graphing software and digital tools as appropriate |
| Victoria | Victorian Curriculum F-10 | Year 9 Maths: closest match in Algebra. Use this page as a VIC-aligned practice and worksheet reference. |
| NSW | NSW Curriculum | Stage 5 Maths: closest content focus for And graph quadratic functions, solve quadratic equations graphically and numerically... and related outcomes. |
| United States | Common Core / NGSS | Grade 9 Common Core Mathematics/ELA closest topic match for And graph quadratic functions, solve quadratic equations graphically and numerically.... |
| England / UK | National Curriculum | Key Stage 3 / Year 9: closest programme-of-study match for And graph quadratic functions, solve quadratic equations graphically and numerically.... |
| Canada | Provincial and territory curricula | Grade 9 closest topic match. Canada varies by province, so use this as a broad Ontario/BC-style learning outcome reference. |
| New Zealand | New Zealand Curriculum | Level 5 Maths: closest achievement-objective topic for And graph quadratic functions, solve quadratic equations graphically and numerically.... |
| India | NCERT / CBSE | Class 9 closest NCERT/CBSE topic match for And graph quadratic functions, solve quadratic equations graphically and numerically.... |