The vertex of a quadratic curve is the maximum orminimum. A quadratic curve has either a maximum or minimum, and onlyhas one. Completing the square makes it possible to find the maximumor minimum value of a quadratic function without sketching it. Westart with an expressionwhichwe want to express in the form The vertex is thenIfthisis a minimum and ifitis a maximum.

Example: find the vertex of the graph for theexpression

Equating coefficients of

Equating coefficients of

Equating constant terms:

Henceincompleted square form is

The vertex is

This is shown below.