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A quadratic function can only have either a maximum or a minimum point, not both. The shape of the graph, which is a parabola, determines this: if the parabola opens upwards (the coefficient of the (x^2) term is positive), it has a minimum point; if it opens downwards (the coefficient is negative), it has a maximum point. Therefore, a quadratic function cannot exhibit both extreme values simultaneously.
The Catenary and Parabola are different curves that look similar; they are both "U" shaped and symmetrical, increasing infinitely on both sides to a minimum.
It has an absolute minimum at the point (2,3). It has no maximum but the ends of the graph both approach infinity.
maximum and minimum are both (-b/2a , c - (b^2/4a))
They both have an arc shape.