3. 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
4. Geometrically:
| x | = the distance of x from zero.
Algebraically:
x, for x > 0
| x | =
-x for x < 0
Algebraically:
x, for x > 0
| x | =
-x for x < 0
5. Find | x | when x has the following values:
-2, 5, .06, 0 , -⅞
x -2 5 .06 0 -⅞
| x |
6. 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:
eithe
r
-
7. 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
8. 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
9. 2
x
Graph the points
Use your calculator to
complete the graph
Complete the following table:
x
0
4
-4
9
-9
16
-16
10. 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
2
y x=
2
x
What conclusion can you draw about the solutions to
and | x | ?
11. Absolute Value- Square Root Theorem
For all real numbers x, = | x |
2
x
What does
this mean?
The square root of a squared expression is the
as the absolute value of the expressionsame
12. Example 1 : Solve the following -
2
x = 72
| x | = 72
therefore: x = 72 or x = - 72
x = or x = -
2
72x =
15. 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?
16. ClosureClosure
• The |x| is
– Geometrically:
– Algebraically:
• What can be said about
• How do you solve |2y + 4| = 16?
• How do you solve 4a2
= 28?
2
x and x
17. 17
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If Yes ,Join Dreams School “Campaign for
Female Education”
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because “When someone takes away your
pens you realize quite how important
education is”.
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your one click can make her smile.
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