Docstoc

Absolute value_ Square Roots and Quadratic Equations

Document Sample
Absolute value_ Square Roots and Quadratic Equations Powered By Docstoc
					Chapter 6: Quadratic
    Functions
Lesson 6-2: Absolute Value,
Square Roots, and Quadratic
        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
                       Use your calculator to
     -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
                   Use your calculator to
    -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?

				
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views:4
posted:6/28/2012
language:
pages:15