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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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Help us in bringing a change in a girl life, because “When someone takes away your pens you realize quite how important education is”.
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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