Vertex calculator

Find the vertex, axis of symmetry, and vertex form of any quadratic. Enter a quadratic expression or equation below.

f(x) =

The vertex of a parabola y = ax² + bx + c is the highest or lowest point. If a > 0, it's a minimum (opens up). If a < 0, it's a maximum (opens down).

x-coordinate: h = −b/(2a)

y-coordinate: k = f(h) = c − b²/(4a)

Vertex form: y = a(x − h)² + k

For y = x² − 4x + 3: a = 1, b = −4, c = 3.

h = −(−4)/(2×1) = 2. k = 3 − 16/4 = −1.

Vertex: (2, −1). Vertex form: (x − 2)² − 1.

The axis of symmetry is the vertical line x = h that passes through the vertex. The parabola is symmetric about this line.

Another way to find vertex form: take y = x² − 4x + 3, rewrite as y = (x² − 4x + 4) − 4 + 3 = (x − 2)² − 1. The vertex is read directly: (2, −1).