Calculating Zeros

The x-coordinate of the intersection of a graph with the x-axis is called the zero. A zero is thus present exactly when the y-coordinate is zero.

Examples

Task: Calculate the zeros of the functions.

$f(x)=x^{ 2 }$

1. Set function equal to zero

   $x^2=0$

2. Solve equation for $x$

   $x^2=0\quad|\sqrt{}$
   $x_{ N }=0$

$g(x)=x^2+1$

1. Set function equal to zero

   $x^2+1=0$

2. Solve equation for $x$

   $x^2+1=0\quad|-1$
   $x^2=-1\quad|\pm\sqrt{}$
   $x_{ N }=\sqrt{ -1 }$ => not defined (there is no zero)

$h(x)=x^2-4$

1. Set function equal to zero

   $x^2-4=0$

2. Solve equation for $x$

   $x^2-4=0\quad|+4$
   $x^2=4\quad|\pm\sqrt{}$
   $x_{ N1 }=-\sqrt{ 4 }=-2$
   $x_{ N2 }=+\sqrt{ 4 }=2$