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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 *x*_{1} and *x*_{2} use the abc-formula

As a result

The *x*-coordinate of the summit is exactly midway between *x*_{1} and *x*_{2}, and for that applies

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