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The minimum or maximum point of a quadratic graph, where the curve changes direction.

The single minimum or maximum point of a quadratic graph, where the curve changes direction.

The turning point is the lowest or highest point, not necessarily the y-intercept.

The maximum or minimum point at which a curve changes direction.

Give roots as $x$ -values, but give intercepts and turning points as coordinates when coordinates are requested.

In $a(x-h)^2+k$ , the turning point is . If the form is , it is , not .

The minimum or maximum point at which a quadratic curve changes direction.

A vertical line through the turning point is the line of symmetry.

A point where a graph changes from rising to falling or from falling to rising.

Completing the square locates the turning point in all three cases.

A highest or lowest point where a curve changes direction.

The midpoint-of-the-roots method requires two real roots. Completing the square still locates the turning point when there are no real roots.

Turning point