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5.1 – Introduction to Quadratic Functions

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					5.1 – Introduction to
Quadratic Functions
Objectives: Define, identify, and graph quadratic
functions.
            Multiply linear binomials to produce a
quadratic expression.
Standard: 2.8.11.E. Use equations to represent curves.
I. Quadratic function is any function that
can be written in the form f(x)= ax2 + bx + c,
where a ≠ 0.
   Ex 2. Let f(x) = (2x – 5)(x - 2). Show that f
    represents a quadratic function. Identify
    a, b, and c when the function is written
    in the form f(x) = ax2 + bx + c.
   FOIL  First – Outer – Inner – Last

 (2x – 5)(x – 2) = 2x2 – 4x – 5x + 10
                      2x2 – 9x + 10
a = 2, b = -9, c = 10
   II. The graph of a quadratic function is called a
    parabola.
   Each parabola has an axis of symmetry, a line that
    divides the parabola into two parts that are mirror
    images of each other.
   The vertex of a parabola is either the lowest point on
    the graph or the highest point on the graph.
                    Axis of
                   Symmetry

                    Vertex
Example 1
Example 2
   Ex 2. Identify whether f(x) = -2x2 - 4x + 1 has a
    maximum value or a minimum value at the vertex.
    Then give the approximate coordinates of the
    vertex.

   First, graph the function:

   Next, find the maximum value of the parabola (2nd,
    Trace):

   Finally,
III. Minimum and Maximum
Values

   Let f(x) = ax2 + bx + c, where a ≠ 0.
    The graph of f is a parabola.
     If a > 0, the parabola opens up and
      the vertex is the lowest point. The y-
      coordinate of the vertex is the
      minimum value of f.
     If a < 0, the parabola opens down
      and the vertex is the highest point.
      The y-coordinate of the vertex is the
      maximum value of f.
   Ex 1. State whether the parabola opens up or down
    and whether the y-coordinate of the vertex is the
    minimum value or the maximum value of the
    function. Then check by graphing it in your Y =
    button on your calculator. Remember: F(X) means
    the same thing as Y!
   a. f(x) = x2 + x – 6   Opens up, has minimum value
   b. g(x) = 5 + 4x – x2 Opens down, has maximum value
   c. f(x) = 2x2 - 5x + 2 Opens up, has minimum value
   d. g(x) = 7 - 6x - 2x2 Opens down, has maximum value
   Homework: page 278 # 14-40 even

				
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posted:9/24/2012
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