1
General Form
A quadratic expression has the highest power of 2 with only one variable:
$$f(x) = ax^2 + bx + c \quad (a \neq 0)$$
2
Shape & Turning Point
The coefficient $a$ determines the curvature and extreme point:
- $a > 0$: Opens upward ($\bigcup$), has a minimum point.
- $a < 0$: Opens downward ($\bigcap$), has a maximum point.
3
Axis of Symmetry & Roots
The vertical line dividing the parabola symmetrically is given by:
$$x = -\frac{b}{2a} \quad \text{or} \quad x = \frac{x_1 + x_2}{2}$$
SPM Examiner Warning & Common Pitfalls
- Must set to General Form $= 0$ before factorizing: Students often forget to expand and simplify terms to $ax^2 + bx + c = 0$ before finding roots. Without showing the factorized form $(px + q)(rx + s) = 0$, you lose the $K1$ (Method) mark!
- Calculator Trap: While Casio ClassWiz gives direct roots ($x = 2, x = -3$), you must write the factorization step $(x - 2)(x + 3) = 0$ in SPM Paper 2. Do not jump straight to roots!
- Real-World Restrictions: In length or time word problems ($t \text{ or } x$), negative values must be rejected with the statement: *"Since length cannot be negative, $x = \dots$"*.