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10.notebook                                                                            September 18, 2012


              Objectives: Equation of a line, rational denominators, completing the square




                                                                                                            1
10.notebook                                                                   September 18, 2012



              Horizontal Line
              m =
              equation:

              Vertical Line
              m = 
              equation:


              1. Find the slope­intercept form of the equation of the line 
              that passes through points (­3, 2) and (4, ­3).




                                                                                                   2
10.notebook                                                               September 18, 2012



              2. Find the equation of the line that passes through (­2, 5) 
              and is perpendicular to the line 3y = ­4x + 2.




                                                                                               3
10.notebook                                                       September 18, 2012



              3. Find the equations of lines (a) and (b).



                                                   (b)



                                                            (a)




                                                                                       4
10.notebook                                                                                       September 18, 2012

          Rational Numbers ­ a number that can be written as a fraction or a decimal that ends or repeats


              Examples:        4            4                1            13              111
                               1            2                4             3               99

                      ­6.4               0.0021              ­122      4.1632       8.3       0.0


              Irrational Numbers ­ decimals that never end or repeat

              Examples:        π         e         √142 ∛13            ∜65




                                                                                                                       5
10.notebook                                    September 18, 2012


              Rationalize the Denominator

              4. Simplify:     4 + √3
                                     2 ­ 3√3




                                                                    6
10.notebook                                September 18, 2012


                                3      5
              5. Simplify: 2 ­ i  + 2i
                              ­2i + 4




                                                                7
10.notebook                                                 September 18, 2012


              Completing the Square

               x2 + 6x + 9 =           x2 ­ 10x + 25=
              (x + 3)2                (x ­ 5)2 
                        1
               2
              x  ­ x +     =
                        4              x2 + 4x +   4  =
                   1 2
              (x ­   )  
                   2
                                               5       25
                                      (x +   )2 
                                             2
                                             5




                                                                                 8
10.notebook                                                      September 18, 2012


              6. Solve ­x + 3x2 = ­5 by completing the square.




                                                                                      9

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Lesson 10

  • 1. 10.notebook September 18, 2012 Objectives: Equation of a line, rational denominators, completing the square 1
  • 2. 10.notebook September 18, 2012 Horizontal Line m = equation: Vertical Line m =  equation: 1. Find the slope­intercept form of the equation of the line  that passes through points (­3, 2) and (4, ­3). 2
  • 3. 10.notebook September 18, 2012 2. Find the equation of the line that passes through (­2, 5)  and is perpendicular to the line 3y = ­4x + 2. 3
  • 4. 10.notebook September 18, 2012 3. Find the equations of lines (a) and (b). (b) (a) 4
  • 5. 10.notebook September 18, 2012 Rational Numbers ­ a number that can be written as a fraction or a decimal that ends or repeats Examples:   4    4 1    13 111 1    2 4     3    99 ­6.4 0.0021 ­122 4.1632       8.3       0.0 Irrational Numbers ­ decimals that never end or repeat Examples: π e √142 ∛13 ∜65 5
  • 6. 10.notebook September 18, 2012 Rationalize the Denominator 4. Simplify:     4 + √3                        2 ­ 3√3 6
  • 7. 10.notebook September 18, 2012 3 5 5. Simplify: 2 ­ i  + 2i    ­2i + 4 7
  • 8. 10.notebook September 18, 2012 Completing the Square  x2 + 6x + 9 =  x2 ­ 10x + 25= (x + 3)2  (x ­ 5)2  1 2 x  ­ x +     = 4  x2 + 4x +   4  = 1 2 (x ­   )   2          5       25 (x +   )2  2 5 8
  • 9. 10.notebook September 18, 2012 6. Solve ­x + 3x2 = ­5 by completing the square. 9