Mathematics · Grades 10–12
Axis of symmetry
The vertex lies on this vertical axis for y = ax² + bx + c.
The key idea
The vertex lies on this vertical axis for y = ax² + bx + c.
x = −b/(2a), a ≠ 0
Worked examples
The graph y = 1x² + 33x + 7 has axis x = k. Find k.
k = −33/(2 × 1) = -33/2
-33/2
The graph y = 1x² + 3x + 8 has axis x = k. Find k.
k = −3/(2 × 1) = -3/2
-3/2
Try it yourself
The graph y = 10x² + 23x + 2 has axis x = k. Find k.
The graph y = 1x² + 25x + 9 has axis x = k. Find k.
Check your understanding
Answers and marking notes
- -23/20
k = −23/(2 × 10) = -23/20
- -25/2
k = −25/(2 × 1) = -25/2
Further reading and review references
These are reference links, not copied exercises, institutional endorsement or proof of independent review.
Learning preview · teacher review required. Grade bands are approximate, not official curriculum alignment.