The zero point deals with functions and their properties and progressions. The zero is the x-value that is inserted into a function and returns the function value "zero". The number of zeros always depends on the function f.

There aredifferent methods for calculating the zeros, which always depend on the function f. The following calculation methods contain both an explanation and at least one example.

The zero of a linear function

Linear functions are constructed as follows: y = mx a



(x) = y = 3x 9


(x) = y = 51x 46

To calculate the zero, set the function f(x) = 0. Following this method gives the following results for the zeros:


= 3x 9 | - 9


9 = 3x | : 3


3 = x


= 51x 46 | - 46


46 = 51x | : 51


0.90 = x

The zero of a quadratic function

Quadratic equations such as x2 2x 1 = 0 are always solved for x, so that the so-called PQ formula

is used.

This means that the formula x2 px q = 0 is used for the equation, resulting in the solution with the following formula:

x1/2 =


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