Vertex of a Parabola
=
Tap a term to see what it means, or .
Calculate
Example: a ball is thrown upward, and its height in metres after t seconds is h(t) = −5t² + 20t + 1. When does it reach its highest point, and how high? Change the coefficients of ax² + bx + c to work out your own case.
Step by step
What each term means
- Vertex (V)
- The parabola's turning point: the lowest, if a > 0, or the highest, if a < 0.
- Vertex x (−b/2a)
- Where the vertex sits on the x axis. The parabola is symmetric about the vertical line through it, and the roots, when they exist, are the same distance away on either side.
- Vertex y (−Δ/4a)
- The function's maximum or minimum value, with Δ = b² − 4ac. In vertex form, f(x) = a(x − h)² + k, the vertex (h, k) shows up directly.