How to find max and min of a quadratic function

A parabola, a graph of a quadratic function, cannot have a maximum vertex and a minimum vertex at the same time because of the shape of the graph.  A parabola is a u-shaped graph.  The vertex of the parabola is the point where the u changes direction; if it was increasing, it starts to decrease, and if it was decreasing, it starts to increase.  Since a parabola only changes direction once, there will either be a minimum or a maximum, not both.

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