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Year 11 · Functions & Graphs
Vertex, axis and discriminant of a parabola
A parabola y = ax² + bx + c has a turning point (vertex), an axis of symmetry and a discriminant that counts its roots.
How to do it
- Axis of symmetry: x = −b ÷ 2a. The vertex sits on it.
- Discriminant Δ = b² − 4ac: positive means 2 roots, zero means 1, negative means none.
Worked example
What is the vertex (turning point) of y = -x² − 2x − 7?
The x-coordinate of the vertex is −b ÷ 2a = 2 ÷ -2 = -1. Substitute back to get y = -6. Vertex: (-1, -6).
Answer: (-1, -6)
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Watch outA positive a opens upwards: the vertex is a minimum.
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