FUN008 · Functions & graphs · Classes 10–12
Cubic Functions
y = ax³ + bx² + cx + d. It can have up to 3 real roots and 2 turning points.
Cubic Functions📐 Formula
Turning points where 3ax² + 2bx + c = 0
✏️ Worked example
y = x³ − 3x: roots 0, ±√3 ≈ ±1.73; turning points at x = ±1.
🌍 Where it is used
Volume of boxes, roller-coaster tracks and animation curves.
❓ Quick check
Maximum number of real roots of a cubic: