Section 2'5 Quadratic Functions Maxima and Minima Main Concepts

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Section 2.5Quadratic Functions Maxima and
Minima Main Concepts

• Different Forms of Quadratic Functions
• Maximum or Minimum Values
• Quadratic Formula
• Vertex Formula
• Graphing to find Max/Min

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Forms of Quadratic Functions

• Quadratic Function
• agt0 parabola opens up
• alt0 parabola opens down
• c is y-intercept
• Standard Form
• Switch forms by completing the square
• a is the same as above
• (h,k) is coordinates of vertex of parabola.
• Shifted h units right and k units up.

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Completing the Square
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Completing the Square Another Example
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Completing the Square More Examples
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Completing the Square More Examples
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Completing the Square Quadratic Formula
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Completing the Square Quadratic Formula
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Maxima and Minima of Quadratic Function
The maximum value of f(x) occurs at If agt0,
this is a minimum and the y-value is If alt0,
this is a maximum and the y-value is
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Maxima and Minima of Quadratic Function
Find the minimum value of this parabola. Draw
a nice graph of it.
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Maxima and Minima of Quadratic Function
This gives the height of a baseball after it is
hit x feet away from the plate. Find its
maximum height. Draw a nice graph of it.
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Other Forms of a Quadratic Function
Standard Form vertex at (h,k) y-intercept at
yc Factored Form x-intercepts at x1 and
x2 max/min occurs half way between
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Find the minimum value of the following functions
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Find the maximum value of the following function.
It describes the height of an object thrown
vertically at an initial speed of 60 feet per
second.
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67 The number of cars that can safely pass a
given point each minute if they are each
traveling s mph is modeled by
Find the optimal speed
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63 The effectiveness of a commercial depends on
how many times a viewer watches it. An
advertising agency found that the effectiveness E
is measured on a scale of 0 to 10, and n is the
number of viewings, then
Find the optimal number of views
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65 The number of apples produced by each tree in
an apple orchard depends on how many trees are
planted per acre. If n trees are planted, each
tree makes 900-9n apples. How many trees should
be planted to maximize the total number of apples
per acre?