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Minimum and maximum

A parabola has a minimum or a maximum value. Mathematically you call this in both cases the top. A parabola is a quadratic function, that you can describe with

 


Explanation

If the convex side points downwards, then a > 0, and the parabola has the form

The coordinates of the top can be calculated in different ways. It depends on how advanced you are in mathematics.

 


Quadratic formula

The x-coordinate of the top can be calculated quickly with the formula

For the intersection points of a second-degree function with the x-axis, y = 0, and thus

To calculate the zeroes x1 and x2 use the abc-formula

As a result

The x-coordinate of the summit is exactly midway between x1 and x2, and for that applies

If you substitute this in the second-degree function, you will find the y-coordinate of the top.

 


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