The Vertex of a Quadratic Graph

The vertex of a quadratic curve is the maximum or minimum. A quadratic curve has either a maximum or minimum, and only has one. Completing the square makes it possible to find the maximum or minimum value of a quadratic function without sketching it. We start with an expressionwhich we want to express in the formThe vertex is thenIfthis is a minimum and ifit is a maximum.

Example: find the vertex of the graph for the expression

Equating coefficients of

Equating coefficients of

Equating constant terms:

Hencein completed square form is

The vertex is

This is shown below.

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