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.

i

Method

1. Set function equal to zero ($x_{ N } \Leftrightarrow f(x_N)=0$)
2. Solve equation for $x$

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 $x$

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