This document outlines an inquiry into decision-making models and their use of relationships. It discusses key concepts in algebra like linear, nonlinear and cubic functions. A concept map shows relationships between algebraic concepts. The document proposes investigating cubic roots and their real-world applications, including hyperbolas. It connects algebraic concepts like parabolas, circles, and hyperbolas to the Victorian curriculum and potential applications in physics, engineering, and architecture.

1. XXXXXX Inquiry
James Parish (Option 1)

2. Overarching Inquiry
• Decision-making can be improved by using a model to represent
relationships

3. Definition of Keywords
• Decision-making
• xxxxx
• Model
xxxxxxx
• Relationships
• xxxxxxxxxx

4. Curiosities (Algebra, Linear Algebra, Non-
linear Algebra
• Factual
xxxxxx
• Conceptual
• xxxxx
• Debatable
• xxxxxx

5. Concept Map of Algebra
Algebra
Linear Algebra
Non-Linear Algebra
Y=mx+x
M = r x Sy/Sx
Rate of change
Acceleration (Gradient of a speed
time graph)
Quadratics Binomial Theorem
Remainder Theorem
Geometric Progression
Arithmetic Progression
Direct and Indirect
proportion
Parabolas
Hyperbolas
Circles
Engineering

6. NRICH Task Investigation – Cubic Roots
• Prelude to our inquiry
• Why have I picked this investigation?
• I am interested in cubic roots and the relevance in the real world
applications. There are also very interesting interpretations of the
cubic equations which offer a variety of solutions. In this context, I am
curious about hyperbolas and………

7. Answers to my investigation

8. Key Concepts covered in the investigation
• Please insert concept map here

9. Future Implications
• How does my investigation connect to real world situations?

10. Real life applications connecting to Algebra
Content in the Vic Curriculum

11. 28.(A - Parabolas) Explore the connection between algebraic and graphical
representations of relations such as simple quadratic, reciprocal, circle and
exponential, using digital technology as appropriate (10)
28.(B - Circles) Explore the connection between algebraic and graphical representations
of relations such as simple quadratic, reciprocal, circle and exponential, using digital
technology as appropriate (10)
28.(C - Exponential relationships) Explore the connection between algebraic and
graphical representations of relations such as simple quadratic, reciprocal, circle and
exponential, using digital technology as appropriate (10)
28.(D - Hyperbolas) Explore the connection between algebraic and graphical
representations of relations such as simple quadratic, reciprocal, circle and
exponential, using digital technology as appropriate (10)

12. (Parabolas) Explore the connection between algebraic and graphical
representations of relations such as simple quadratic, reciprocal, circle
and exponential, using digital technology as appropriate (10)
• 1) Explain the concept
• 2) Offer different scenarios and solutions
• Use software like Desmos to illustrate each of the solutions and
concepts
• 3) Possible real-life applications (Trajectory, bridges, max and min
capacity of packaging, circles are used to map forces, speed,
acceleration in physics)

13. (B - Circles) Explore the connection between algebraic and graphical
representations of relations such as simple quadratic, reciprocal, circle
and exponential, using digital technology as appropriate (10)
• 1) Explain the concept
• 2) Offer different scenarios and solutions
• Use software like Desmos to illustrate each of the solutions and
concepts
• 3) Possible real-life applications (Trajectory, bridges, max and min
capacity of packaging, circles are used to map forces, speed,
acceleration in physics)

14. Binomial Theorem (Permutations and
Combinations) (Optional)

15. Lesh’s Translation Model (Reflection)

16. Connection to my inquiry
• How are quartic functions relevant to modern day engineering?
• How can we connect Arithmetic and Geometric Progression to
Algebra used in Architecture?

17. Bibliography and References