Foundation and Higher · graph shapes

Four graph shapes
you must recognise.
Check the power.

line, U, S
and two curves

to name any graph, find the —

Highest power

x · x² · x³ · 1 ÷ x

each one has its own shape

shape 1 of 4

Linear

1. Just x, no powers: a straight line.

2. A negative gradient slopes downhill.

✓ y = mx + c

shape 2 of 4

Quadratic

1. Highest power x²: a U shape.

2. Negative x²: it flips to an n shape.

✓ A parabola: one turning point

shape 3 of 4

Cubic

1. Highest power x³: an S-shaped curve.

2. Negative x³: it starts high and ends low.

✓ Up to two turning points

shape 4 of 4

Reciprocal

1. x on the bottom: two separate curves.

2. They get close to the axes, never touch.

✓ No value at x = 0: you cannot ÷ 0

the highest power tells you —

x

a straight line

x²

a U, or an n if negative

x³

an S-shaped curve

1 ÷ x

two curves, never touching the axes

Sketch means shape and key points,
not a table of values.

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