Quadratic Functions and Equations in One Variable
Axis of symmetry
The vertical line through the turning point that divides a parabola into two mirror halves.
| English | Axis of symmetry |
|---|---|
| Bahasa Melayu | Paksi simetri |
| 中文 | 对称轴 |
How it is used
The parabola y = x² − 6x + 5 has its turning point at (3, −4), so its axis of symmetry is the vertical line x = 3; the points (1, 0) and (5, 0) are mirror images across it.
Where it shows up in SPM
Used when sketching and analysing parabolas (Form 4). Paper 2 may ask for the equation of the axis of symmetry, or use symmetry to find a second point or a missing root when only one and the turning point are known.
Don't confuse it with
Open the chapter: Quadratic Functions and Equations in One Variable →
Frequently asked questions
How do I find the axis of symmetry quickly?
The axis of symmetry passes through the turning point, so it is x = h from the form a(x − h)² + k. You can also use x = −b/(2a).
For y = x² − 6x + 5, x = −(−6)/(2×1) = 3.
If I know both roots, where is the axis of symmetry?
It is exactly halfway between the roots. If the roots are 1 and 5, the axis of symmetry is x = (1 + 5)/2 = 3.
This works because the parabola is symmetrical about the vertical line through its turning point.