y = a(x − h)² + k, which shows the vertex (h, k) directly.

Vertex of a Parabola

Finds the turning point (vertex) of y = ax² + bx + c.

h = - \frac{b}{2 a}, k = f (h)

Variables

(h, k): Coordinates of the vertex
a, b, c: Coefficients of the quadratic

Explanation

The parabola is symmetric about the vertical line $x = - \frac{b}{2 a}$ . Substituting this x-value into the function gives the minimum (if $a > 0$ ) or maximum (if $a < 0$ ) value.

Example

For $y = x^{2} - 4 x + 3$ : $h = \frac{4}{2} = 2$ , $k = 4 - 8 + 3 = - 1$ . Vertex $(2, - 1)$ .

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Related formulas

Quadratic Formula

Solves any quadratic equation ax² + bx + c = 0.