• Define the quadratic function, find its vertex in both forms and sketch its graph.
• Use the maximum or minimum value in real-life optimisation.
• Find the zeros of polynomial functions by factoring, completing the square or reading the graph.
• Determine the domain of a rational function, simplify it, and perform the four operations with their restrictions.

Quadratic, Polynomial and Rational Functions
├── 2-1 The quadratic function
│   ├── definition, values, points on the curve
│   ├── vertex form y = a(x - h)² + k
│   ├── equation from the vertex and one point
│   ├── sketch and vertex from the general form
│   └── maximum and minimum applications
├── 2-2 Polynomial functions
│   ├── degree and leading term
│   └── zeros: factoring, completing the square, from the graph
├── 2-3 Rational algebraic functions
│   ├── domain, simplifying
│   └── zeros of a rational function
├── 2-4 Common domain of two functions and equality of functions
└── 2-5 Operations on functions
    ├── addition and subtraction
    ├── multiplication and division
    ├── additive and multiplicative inverses
    └── properties of the operations

💡 High-yield traps

• The vertex of y = a(x − h)² + k is (h, k) — the sign of h is opposite to what appears in the bracket.
• k is a maximum only when a < 0; read the sign of a before answering.
• For the general form use h = −b/(2a); forgetting the minus sign puts the vertex on the wrong side.
• The definition of a quadratic requires a ≠ 0.
• Zeros from the graph touching means even multiplicity, crossing means odd.
• Cancel factors, never terms — (x + 2)/x is already simplest.
• Simplifying does not enlarge the domain; the old restrictions must be restated.
• A zero of a rational function comes from the numerator only, and must not vanish the denominator.
• Division of fractions doubles the restrictions those of the divisor and those created by flipping it.
• Two functions are equal only with the same domain and the same rule.