Higher only · quadratic inequalities

Quadratic
inequality?
Sketch it.

the graph tells you
which side

the numbers where the sign changes —

Critical values

solve it as an equation first

then sketch to choose the region

step 1 of 4

Solve it as an equation

1. Swap the < for = and factorise.

2. These are the critical values.

✓ They are not the answer yet

x² − 2x − 3 < 0

(x + 1)(x − 3) = 0

x = −1  or  x = 3

step 2 of 4

Sketch the curve

1. Mark the critical values on the axis.

2. Positive x²: a U-shape through them.

✓ A rough sketch is enough

step 3 of 4

Less than 0: below

1. < 0 means the curve is below the x-axis.

2. That is between the critical values.

✓ −1 < x < 3: one inequality

step 4 of 4

Greater than 0: above

1. x² − 2x − 3 > 0: above the x-axis.

2. Two separate parts, outside the values.

✓ x < −1 or x > 3: two inequalities

quadratic inequalities —

Solve

= 0 gives the critical values

< 0

below the axis: between them

> 0

above the axis: outside them

≤ or ≥? Same regions,
include the critical values.

The
Maths Habit

Download The Maths Habit app
to test your knowledge