Quadratic Functions by 92m08d4

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									Quadratic Functions


     Section 2.2
             Objectives
• Rewrite a quadratic function in vertex
  form using completing the square.
• Find the vertex of a quadratic function.
• Find x-intercepts and y-intercepts of a
  quadratic function.
• Write a quadratic function given two
  points.
             Objectives
• Solve a word problem involving a
  quadratic function.
• Determine how a function has been
  transformed given an equation or a
  graph.
• Given a description of a transformed
  function, write the equation of the new
  function.
               Vocabulary

•   quadratic function
•   parabola
•   standard form of a quadratic equation
•   completing the square
Given the function below find
the vertex, x-intercepts, and
y-intercepts:
     f (x )  3x  27 x  24
                2
Find a function whose graph is
a parabola with vertex (-2, -9)
and that passes through the
point (-1, -6).
The profit function for a
computer company is given by
    P (x )  x  38x  11
              2


where x is the number of units
produced (in thousands) and
the profit is in thousand of
dollars.
Determine how many
(thousands of) units must be
produced to yield maximum
profit.
    P (x )  x  38x  11
              2
Determine the maximum
profit.
    P (x )  x  38x  11
              2
Determine how many units
should be produced for a
profit of at least 40 thousand
dollars.
      P (x )  x  38x  11
                2
The graph of the function
       y  f (x )  89
can be obtained from the
graph of f(x) by what
transformation?
Given f (x )  x  2


after performing the following
transformations, write the
equation of the new
transformed function:
•reflect over the x-axis
•shift upward 48 units
•shift 85 units to the right

								
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