# Absolute value_ Square Roots and Quadratic Equations

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```					Chapter 6: Quadratic
Functions
Lesson 6-2: Absolute Value,
Equations
Absolute value can be defined as the

distance                     from zero on a

number line.

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

Geometrically:

Algebraically: | x - 3| = 5 means     either

-
x -3 =                 or    x -3 =
Is f : x    | x | a function?

Create a table of values:

|x|
x
Graph the points
0

4

-4

9
-9                complete the graph: The
Absolute Value function is
16                located in:
Math> NUM>1: abs(
-16
Square Root

The square root or            radical              sign

stands for the             positive                 square root of a
real number.

The      4      stands for the positive value or       2

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

which equals
-2
Complete the following table:

x          2
Graph the points
x
0

4

-4

9
-9
complete the graph
16

-16
fx = x
8
fx = x
8

6
6

4
4

2
2

-10          -5                5    10
-10          -5            5   10

y x
-2
-2

y x              2
-4
-4

-6
-6

What conclusion can you draw about the solutions to

2       and   |x|?
x
Absolute Value- Square Root Theorem
2
For all real numbers x,               x       =|x|
What does
this mean?

The square root of a squared expression is the

same           as the absolute value of the expression
Example 1 : Solve the following -
x  72
2

x   2        =   72

|x|              =   72

therefore:           x    =   72   or x = -   72

x=        or x = -
Example 2: Solve the following -

34  2 y  12
Example 3: Solve the following -

3 x  18
2
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?
Closure
• The |x| is
– Geometrically:
– Algebraically:
2
• What can be said about       x       and   x
• How do you solve |2y + 4| = 16?

• How do you solve 4a2 = 28?

```
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 views: 4 posted: 6/28/2012 language: pages: 15