Watch out
Reading the x-coordinate with the wrong sign from a bracket.
Scottish National 5 Mathematics
National 5 Maths Quadratic functions
Recognise, sketch and interpret quadratic functions in factorised and completed-square forms.
Formula reference
Check the National 5 rules and formulae linked to this topic.
Which method?
Match exam clues to a suitable method.
Before you start
- Use factorised form for roots.
- Decide whether a calculator supports the method; exact working may still be required.
- Read the command word, record the units or requested form, and make the final answer match it.
Explanation
Quadratic functions is an assessed part of Scottish National 5 Mathematics in the algebra area. Recognise, sketch and interpret quadratic functions in factorised and completed-square forms.
Use factorised form for roots.
Use completed-square form for the turning point and axis of symmetry.
Plot the y-intercept and use symmetry to make a clear sketch.
The interactive bank below mixes direct skills, reverse questions, interpretation and contextual reasoning rather than repeating one number pattern.
Visual support
Parabola features
Key formulae and rules
- y = a(x − m)(x − n)
- y = k(x + p)² + q
Check
Check roots by substitution and compare the turning point or discriminant conclusion with the equation's graph.
Exam tip
Keep equations aligned line by line so method marks remain visible, especially through sign and bracket changes.
Worked examples
Worked example 1
Quadratic functions worked example
State the turning point and axis of y = 2(x − 3)² − 5.
- The squared expression is least when x = 3.
- Then y = −5
Answer: Turning point (3, −5); axis x = 3
Watch out
- Reading the x-coordinate with the wrong sign from a bracket.
- Drawing a scale graph when only a labelled sketch is required.