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Solving Quadratic Functions by Graphing

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Solving Quadratic Functions by Graphing Powered By Docstoc
					Investigating Graphs
         of
Quadratic Functions
                   Objectives

• You will be able to describe how the
  values of the coefficients of a
  quadratic function affect the graph.

• You will be able recognize the graph
  of a quadratic function by it’s
  equation.

Algebra I Honors   Graphing Quadratic Functions   Pankowski
                     Review
       How to graph a quadratic function by
       hand:
       1. Find the x-coordinate of the vertex: -
       b/(2a).
       2. Make a table of values, using x-values to
       the left and right of the vertex.
       3. Plot the points and connect them with a
       smooth curve to form a parabola.


Algebra I Honors     Graphing Quadratic Functions   Pankowski
                        Example:
                    y  x  2x  3
                               2

                                                        a=     1
x-coordinate of vertex  (2) /(2 *1)                  b=    -2
                                2 /2                   c=    -3
                               1
      
y-coordinate of vertex  12  2(1)  3
                                1 2  3
                   
                                1 3             Vertex    (1,4)
                                4

Algebra I Honors        Graphing Quadratic Functions         Pankowski
                              y  x  2x  3
                                      2

     Pick values to left and right of Vertex (equidistant
     from vertex)
-The vertex is located at (1,-4).

-One unit to the right
          
and left of x=1 are x=0
and x=2.

-Two units to the right
and left of x=1 are x=3
and x=-1.
-Make a table by
substituting these x-values
into your function to find
their corresponding y-
values.
    Algebra I Honors           Graphing Quadratic Functions   Pankowski
                               y  x  2x  3
                                          2

           x 1                        x2                        x0
           y  12  2(1)  3           y  2 2  2(2)  3         y  0 2  2(0)  3
           y  1 2  3                y 443                   y  00 3
           y  1 3                   y  0 3                   y  0 3
           
           y  4                      y  3                     y  3
           Vertex  (1,4)             B  (2,3)                 C  (0,3)

           x  1                      x3
        y  (1) 2  2(1) 
                              3        y  32  2(3)  3 
          y  1 2  3                y  96 3
          y  3 3                     y  3 3
          y0                          y0
          D  (1,0)                   E  (3,0)

     Algebra I Honors              Graphing Quadratic Functions              Pankowski
                       Table of Values
             Point                    X                  Y

           Vertex                     1                  -4

                   B                  2                  -3

                   C                  0                  -3

                   D                 -1                  0

                   E                  3                  0

Algebra I Honors          Graphing Quadratic Functions        Pankowski
                Plot the Points and
              Connect a Smooth Curve




Algebra I Honors    Graphing Quadratic Functions   Pankowski
                   Investigation
• Open your laptop

• Open the file on your desktop labeled
  “Multimedia1a_Dynamic_Worksheet_EHP.h
  tml”

• Answer the questions on the worksheet by
  investigating using the sliders
Algebra I Honors     Graphing Quadratic Functions   Pankowski

				
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