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Absolute Value, Square Roots, and Quadratic Equations

Absolute value can be defined as the

from zero on a

number line.

| 3 | is the point that is 3 units away from

distance

Zero

Geometrically:

| x | = the distance of x from zero.

Algebraically:

x, for x > 0 | x | =

-x for x < 0

Find | x | when x has the following values: -2, 5, .06, 0 , -⅞

x -2 5 .06 0 -⅞

| x |

Solve: | x - 3| = 5 can be read as "x is 5 units from 3 in

either direction"

Algebraically: | x - 3| = 5 means

x -3 = or x -3 =

Geometrically:

either

-

Graph the points

Use your calculator to complete the graph: The Absolute Value function is located in:

Math> NUM>1: abs(

Is f : x | x | a function?

Create a table of values:

x | x |

0

4

-4

9

-9

16

-16

The square root or sign

stands for the square root of a real number.

4 stands for the positive value or

Square Root

radical

The

positive

2

To find the negative square root you need to write: - 4

which equals -2

2xGraph the points

Use your calculator to complete the graph

Complete the following table:

x

0

4

-4

9

-9

16

-16

8

6

4

2

-2

-4

-6

-10 -5 5 10

f x = x

y x

8

6

4

2

-2

-4

-6

-10 -5 5 10

f x = x

2y x

2x

What conclusion can you draw about the solutions to

and | x | ?

Absolute Value- Square Root Theorem

For all real numbers x, = | x |

2xWhat does this mean?

The square root of a squared expression is the

as the absolute value of the expressionsame

Example 1 : Solve the following -

2x = 72

| x | = 72

therefore: x = 72 or x = - 72

x = or x = -

2 72x

Example 2: Solve the following -

34 2 12y

Example 3: Solve the following -

23 18x

Example 4:Example 4: A square and a triangle have the same area. The triangle has base 7 cm. And altitude 6 cm. What is the length of a side of the square?

ClosureClosure• The |x| is

– Geometrically:– Algebraically:

• What can be said about

• How do you solve |2y + 4| = 16?

• How do you solve 4a2 = 28?

2x and x

17

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Just Click on any advertisement on the page, your one click can make her smile. We our doing our part & u ?

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