Recognise, plot and draw non-linear graphs. Master the shapes examiners expect you to know.
PANEL A: THE VISUAL TOY — Cubic Snake
a (x³ coefficient)1
d (constant)0
Probe x-value1
PANEL B: THE LOGIC TRACK
CUBIC GRAPH IDENTIFICATION
Positive coefficient of x³: The curve goes from bottom-left to top-right — like a snake slithering uphill.
Every cubic has this characteristic 'S' shape. It always crosses the y-axis at (0, d).
EXAMINER TRAP
Don't confuse cubics with quadratics! A cubic has an x³ term and ALWAYS extends to both +∞ and -∞ on the y-axis. Quadratics don't — they have a turning point.
QUICK IDENTIFICATION GUIDE
Positive a: Starts low-left, ends high-right
Negative a: Starts high-left, ends low-right
y-intercept always at (0, d)
PANEL C: THE DYNAMIC SOLVER
TABLE OF VALUES: y = x³
x
-2
-1
0
1
2
y
-8
-1
0
1
8
STEP-BY-STEP SUBSTITUTION
Step 1: Sub x = -2
1(-2)³ = -8
= -8
Step 2: Sub x = 0
1(0)³ = 0
= 0
Step 3: Sub x = 2
1(2)³ = 8
= 8
Edexcel 4MA1 · Section 3.3A: Recognise, plot and draw graphs of cubic and reciprocal functions · Gen Z Study
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