body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

{{ 'ml-label-loading-course' | message }}

{{ toc.name }}

{{ toc.signature }}

{{ tocHeader }} {{ 'ml-btn-view-details' | message }}

{{ tocSubheader }}

{{ 'ml-toc-proceed-mlc' | message }}

{{ 'ml-toc-proceed-tbs' | message }}

An error ocurred, try again later!

Chapter {{ article.chapter.number }}

{{ article.number }}.

{{ article.displayTitle }}

{{ article.intro.summary }}

Show less Show more

{{ ability.displayTitle }}

Lesson Settings & Tools

	{{ 'ml-lesson-number-slides' \| message : article.intro.bblockCount }}
	{{ 'ml-lesson-number-exercises' \| message : article.intro.exerciseCount }}
	{{ 'ml-lesson-time-estimation' \| message }}

{{ item.file.title }}
{{ presentation }}

No file copyrights entries found

Concept

Zero - Function

Any input value in the domain of a function whose output equals

0

is known as a zero or root of the function. A function can have more than one zero or no zeros at all. Graphically, the zeros of a function are the

x

coordinates of the

x -

The function 0.4*(x+2)*(x-1)*(x-2) with zeros at (-2,0), (1,0), and (2,0)

Consider the following function as an example.

f (x) = 2 x + 1

To find the zeros of a function, substitute the

0

for the output

f (x)

in the function rule and solve the resulting equation for

x .

f (x) = 2 x + 1

$f (x) = 0$

0 = 2 x + 1

▼

Solve for

x

$LHS - 1 = RHS - 1$

- 1 = 2 x

$LHS / 2 = RHS / 2$

\frac{- 1}{2} = x

MoveNegNumToFrac

Put minus sign in front of fraction

- \frac{1}{2} = x

Rearrange equation

x = - \frac{1}{2}

This example function has a zero at

x = - \frac{1}{2}

because

f (- \frac{1}{2}) = 0 .

This can be verified by evaluating the function at this value.

f (x) = 2 x + 1

▼

Evaluate

$x = - \frac{1}{2}$

f (- \frac{1}{2}) = 2 (- \frac{1}{2}) + 1

Multiply

f (- \frac{1}{2}) = - 1 + 1

Add terms

f (- \frac{1}{2}) = 0

Since this is the only solution to the equation, it is also the only zero of the function. If a function does not intercept the

x -

axis, there will be no real solution for the resulting equation when the function rule is set equal to

0 .

In such a case, the function will have no zeros.

Zeros of different functions applet

{{ grade.displayTitle }}

Loading content