Quiz 2

Chatty reference · maths1 week 3

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2026-08-16T00:00:00.000Z
Python Week 1: the first filter for runtime behavior
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ChatGPT archive slice for week 3. # 3.

3. Maths Week 3 — Quadratic Functions

Concepts:
  • Quadratic function
  • Standard form
  • Vertex
  • Axis of symmetry
  • Maximum/minimum
  • Slope
  • Quadratic equation
  • Roots
  • Discriminant
  • Graph interpretation
The fundamental representation:
f(x)=ax2+bx+cf(x)=ax^2+bx+c
Vertex:
xv=−b2ax_v=-\frac{b}{2a}
Patterns:

Pattern M3-1 — Find roots

Given:
ax2+bx+c=0ax^2+bx+c=0
determine xx.

Pattern M3-2 — Determine number/type of roots

Use:
Δ=b2−4ac\Delta=b^2-4ac

Pattern M3-3 — Find maximum/minimum

Determine sign of aa:
  • a>0a>0 → minimum
  • a<0a<0 → maximum

Pattern M3-4 — Recover quadratic from information

For example:
  • vertex + another point
  • roots + another point
  • three points

Pattern M3-5 — Graph ↔ algebra

Given graph → infer:
  • roots
  • vertex
  • direction
  • approximate equation
This representation-switching is exactly the kind of thing I want us to train.
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