Coefficient by djy18697

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									                   Coefficient
    In any term, the coefficient is the
    numeric factor of the term or the
     number that is multiplied by the
                 variable.
                                          Example: 3x
                                    3 is the coefficient of x
Created by Heather Bergman- Jersey Village High School Houston, Texas
                                          Polygon
   A closed plan figure formed by
    three or more segments that
intersect only at their endpoints. In
 a regular polygon, all angles and all
    line segments are congruent.

Created by Heather Bergman- Jersey Village High School Houston, Texas
         Parallel Lines
Lines in the same plane
                                                                                          10
                                                                                          8
                                                                                          6



that never intersect.
                                                                                          4
                                                                                          2

                                                                        -10 -8 -6 -4 -2        2   4   6   8 10


Parallel Lines also have
                                                                                          -2
                                                                                          -4
                                                                                          -6


the same slope.
                                                                                          -8
                                                                                      -10




               y = 3x + 2
               y = 3x – 6
Created by Heather Bergman- Jersey Village High School Houston, Texas
          Complementary
             Angles
         Two angles are complementary if
                their sum in 90.

 a  b  90                                                           a
                                                                            b
Created by Heather Bergman- Jersey Village High School Houston, Texas
           Supplementary
              Angles
          Two angles are supplementary if
                their sum is 180.

 a  b  180                                                          a   b


Created by Heather Bergman- Jersey Village High School Houston, Texas
                             45-45-90
                                  Special Right Triangle


                                                                            x 2
                                            x



Created by Heather Bergman- Jersey Village High School Houston, Texas
                                                                        x
                             30-60-90
                                  Special Right Triangle

                                                                        30
                                                                                  2x
                                                       x 3



Created by Heather Bergman- Jersey Village High School Houston, Texas
                                                                              x
Pythagorean Theorem
    2     2     2
                       a +b =c
Remember these Pythagorean Triples:

3-4-5
                                                                                c
5-12-13                                                                 a

                                                                            b
Created by Heather Bergman- Jersey Village High School Houston, Texas
                                                                Slope
*tells how steeply a line slants
*rise over run
*rate of change         y = 3x – 2
  change in y y
                                                                       Slope
* change in x x


Created by Heather Bergman- Jersey Village High School Houston, Texas
 Perpendicular Lines
  Two lines that intersect to form
            right angles.
y= ½ x + 3                                                                                10



y = -2x – 2
                                                                                          8
                                                                                          6
                                                                                          4
                                                                                          2

                                                                        -10 -8 -6 -4 -2        2   4   6   8 10

Notice the relationship of                                                                -2
                                                                                          -4
their slopes. The product of                                                              -6

their slopes is -1.                                                                       -8
                                                                                      -10

Created by Heather Bergman- Jersey Village High School Houston, Texas
                                                      Mean
             The average of a set of values.


                                    abcd e
                                        5
Created by Heather Bergman- Jersey Village High School Houston, Texas
                                            Median
    The middle value of a set of values
    when all the values are arranged in
                   order.

                                            13, 17, 23, 25, 27
                                            The median is 23.
Created by Heather Bergman- Jersey Village High School Houston, Texas
                                                     Mode
    The values that occurs most often.
    Some sets of data have more than
    one mode, and some have no mode.

                              12, 24, 34, 12, 24, 67
                            12 and 24 are the modes
Created by Heather Bergman- Jersey Village High School Houston, Texas
                                        Percent
   This word literally means “per one
  hundred” and is represented by the
               symbol %.


                                 50% = ½ = .50
Created by Heather Bergman- Jersey Village High School Houston, Texas
Linear Parent Function
         y=x
                                                                        10
                                                                         8
                                                                         6
                                                                         4
                                                                         2

                                                -10 -8 -6 -4 -2               2   4   6   8 10
                                                                         -2
                                                                         -4
                                                                         -6
                                                                         -8
                                                                        -10
Created by Heather Bergman- Jersey Village High School Houston, Texas
                   Quadratic Parent
                      Function
                            2
                        y=x
                                                                             10
                                                                             8
                                                                             6
                                                                             4
                                                                             2

                                                           -10 -8 -6 -4 -2        2   4   6   8 10
                                                                             -2
                                                                             -4
                                                                             -6
                                                                             -8

Created by Heather Bergman- Jersey Village High School Houston, Texas    -10
               Exponential Parent
                   Function
                         x
                     y=b
                       10                                                                  10
                        8                                                                  8
                        6                                                                  6
                        4                                                                  4
                        2                                                                  2

 -10 -8 -6 -4 -2               2    4    6   8 10                        -10 -8 -6 -4 -2        2   4   6   8 10
                        -2                                                                 -2
                        -4                                                                 -4
                        -6                                                                 -6
                        -8                                                                 -8
                      -10                                                              -10



Exponential Growth                                                       Exponential Decay
       b>1                                                                    0<b<1
 Created by Heather Bergman- Jersey Village High School Houston, Texas
                                   Natural
                                   Numbers
       The numbers we use for counting.

          1, 2, 3, 4, 5, 6, 7 . . .
Created by Heather Bergman- Jersey Village High School Houston, Texas
                  Rational Numbers
    Any number that can be expressed
    as the ratio of two integers in the
                  a
           form b where b 0.
                                                                        


                                                                 2
                                                        Example: 3
Created by Heather Bergman- Jersey Village High School Houston, Texas
                                  Constant
                           A term with no variables.

                                                             2
                                                 2x + 3x + 5 = y

                                           The constant is 5.

Created by Heather Bergman- Jersey Village High School Houston, Texas
                                        Integer
                               The numbers in the set

    {. . . . –4, -3, -2, -1, 0, 1, 2, 3, 4. . . .}



Created by Heather Bergman- Jersey Village High School Houston, Texas
                       Exponents
                    Product Property

                                                                            a b
           x *x  x       a                                             b


Created by Heather Bergman- Jersey Village High School Houston, Texas
                  Exponents
               Quotient Property
                                                       a
                                          x      a b
                                            b
                                              x
                                          x
Created by Heather Bergman- Jersey Village High School Houston, Texas
                             Exponents
                           Power Property

                             x 
                                                      b
                                                    a
                                                                        x   a*b



Created by Heather Bergman- Jersey Village High School Houston, Texas
                Exponents
             Negative Exponent
                                                              b        b
                 m  n
                    
                 n  m
Created by Heather Bergman- Jersey Village High School Houston, Texas
                                          Exponents
                                          Zero Power


                              b 1                      0
Created by Heather Bergman- Jersey Village High School Houston, Texas
      Domain of a Function
      The set of input values for which
      the function is defined (x-values).
     10
       9
       8
       7
       6
       5
       4
                                                                        D0 x6
       3
       2
       1

                 1        2       3        4       5        6       7


Created by Heather Bergman- Jersey Village High School Houston, Texas
           Range of a Function
           The set of output values for the
                 function (y values).
     10
       9
       8




                                                                        R0 y9
       7
       6
       5
       4
       3
       2
       1

                 1        2       3        4       5        6       7

Created by Heather Bergman- Jersey Village High School Houston, Texas
   Coordinate Plane                                                     y-axis
                                                                         10

  Origin                                                                  8
                                                                          6
                                                         II               4           I
                                                                          2
                                                                                                     x-axis
                                       -10 -8 -6 -4 -2                        2   4       6   8 10
                                                                         -2
                                                                         -4
                                                        III              -6       IV
                                                                         -8
                                                                        -10
Created by Heather Bergman- Jersey Village High School Houston, Texas
                                                   Range
         The range of a data set is the
       difference between the maximum
              and minimum values.

                                                        4, 10, 2, 5, 7

                                            Range = 10 - 2 = 8
Created by Heather Bergman- Jersey Village High School Houston, Texas
                          Polynomial
      A term or a sum of terms where
    each term is the product of a real-
     number coefficient and a variable
     with a whole-number coefficient.

                                                        3               2
                                            2x + 5x – 3x + 4
Created by Heather Bergman- Jersey Village High School Houston, Texas
          Similar Figures
   Two figures are similar when their
   corresponding angles are congruent
    and their corresponding sides are
               proportional.
                                                                        32


                                                  74

Created by Heather Bergman- Jersey Village High School Houston, Texas
                                           Rotation
   A rotation turns a figure through a
   given angle about a point called its
                 center.                                                                  10
                                                                                          8
                                                                                          6

                            Example:                                                      4
                                                                                          2

        Rotate the given figure                                         -10 -8 -6 -4 -2        2   4   6   8 10
                                                                                          -2
      counterclockwise 90 about
                                                                                          -4
              the origin.                                                                 -6
                                                                                          -8

Created by Heather Bergman- Jersey Village High School Houston, Texas
                                                                                      -10
                                            Variable
               A letter used to stand for a
              quantity that changes in value.



                             x is the variable in 9 – x
Created by Heather Bergman- Jersey Village High School Houston, Texas
                                           Function
        A special relation in which each x
        value (domain) is paired with only
               one y value (range).



Created by Heather Bergman- Jersey Village High School Houston, Texas
     Direct Variation
    A linear function that can be
 expressed in the form y = kx, where
                k  0.



Created by Heather Bergman- Jersey Village High School Houston, Texas
Scientific Notation
        A number expressed in the form
              n
        a x 10 , where n is an integer and
                    1  a  10 .

                                                                        4
                                       3.4 x 10 = 34,000
                                              -4
                                      3.4 x 10 = 0.00034
Created by Heather Bergman- Jersey Village High School Houston, Texas
 Function Notation
    To write a rule in function notation
        you use the symbol f(x) in
                place of y.

  f(x) = 3x – 8 is in function notation.

Created by Heather Bergman- Jersey Village High School Houston, Texas
                                      Relation
     A set of ordered pairs that shows
       how two variables are related.

                     {(2,3), (7,11), (-3, 6), (7,-5)}

Created by Heather Bergman- Jersey Village High School Houston, Texas
   Independent Variable
       The independent variable is the
         input variable or x-variable
     (abscissa) and is listed first in the
                ordered pair.
       “The amount the grass grows depends on the
                    amount of rain.”
          Independent variable-amount of rain
Created by Heather Bergman- Jersey Village High School Houston, Texas
           Dependent Variable
   The dependent variable is the
    output variable or y-variable
(ordinate) and is listed second in the
            ordered pair.
       “The amount the grass grows depends on the
                    amount of rain.”
         Dependent variable-amount grass grows
Created by Heather Bergman- Jersey Village High School Houston, Texas
                                               Mapping
   A diagram that uses arrows and
  numbers in “bubbles” to show the
relationship between the domain and
   x    y
               range. 2          -1
             2                    -1
             4                     6                     TABLE                        5
                                                                                  3
             3                     5                                                  6
             3                    10                                              4
                                                                        MAPPING
                                                                                      10
Created by Heather Bergman- Jersey Village High School Houston, Texas
                   Horizontal Line

Equation:                                                      y=a
Slope :                                                        0
y-Intercept :                                                  a
x-Intercept :                                                  none


Created by Heather Bergman- Jersey Village High School Houston, Texas
                              Vertical Line

Equation:     x=a
Slope : Undefined
y-Intercept : none
x-Intercept: a


Created by Heather Bergman- Jersey Village High School Houston, Texas
                            Y-Intercept
The y-coordinate of the point where a
graph crosses the y-axis.

          The y-intercept
                        is -5.


Created by Heather Bergman- Jersey Village High School Houston, Texas
                           X-Intercept
The x-coordinate of the point where a
graph crosses the x-axis.

          The x-intercept
          is -2.


Created by Heather Bergman- Jersey Village High School Houston, Texas
                                                             Ratio
                 A comparison of two numbers by
                            division.

                  Examples:                                             3:7
                                                                        3
                                                                        5
                      Slope is an example of a ratio.
Created by Heather Bergman- Jersey Village High School Houston, Texas

								
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