How to Find the Vertex of a Parabola

For y=ax²+bx+c with a nonzero, the vertex has x-coordinate −b/(2a). Substitute it to find y.

Example

For y=x²−4x+1, x=2 gives y=−3. Enter x^2-4*x+1. The graph opens upward and is symmetric around x=2.

Check with vertex form

Rewrite the expression as (x−2)²−3. The squared term reaches zero at x=2, confirming the minimum.

Try the Graphing Calculator.