Quadratic Functions

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Quadratic Functions

• are functions with a squared term.

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Quadratic Functions
Quadratic Term
Linear Term
Constant
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Quadratic Functions
The graph is called a PARABOLA.
Parabolas can open UP or
open DOWN.
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Quadratic Functions
Parabolas that open UP have a MIN. Parabolas
that open DOWN have a MAX.
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Quadratic Functions
Parabolas that open UP have a MIN. Parabolas
that open DOWN have a MAX.
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Quadratic Functions
MINs and MAXs ALWAYS occur at the
VERTEX of the Parabola.
The x-coordinate of the VERTEX of any
Parabola _____.
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Quadratic Functions
MINs and MAXs ALWAYS occur at the
VERTEX of the Parabola.
Find the vertex of the parabola with this
equation
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Quadratic Functions
MINs and MAXs ALWAYS occur at the
VERTEX of the Parabola.
Find the vertex of the parabola with this
equation
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Graphing Quadratic Functions

• Calculate and plot the vertex.
• Plot the y-intercept.
• (Let x 0 and solve for y.)
• Make a table of values.
• Connect the points with
  a SMOOTH curve,
  not a series of line segments.

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Example 1-4a
Economics Application
A souvenir shop sells about 200 coffee mugs each
month for 6 each. The shop owner estimates that
for each 0.50 increase in the price, he will
sell about 10 fewer coffee mugs per month. How
much should the owner charge for each mug in
order to maximize the monthly income from their
sales?
Words The income is the number of mugs
multiplied by the price per mug.
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Example 1-4a
Let I(x) equal the income as a function of x.
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Example 1-4a
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Example 1-4a
This means that the shop should make 4 price
increases of 0.50 to maximize their income.
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Example 1-4a
What is the maximum monthly income the owner can
expect to make from these items?
Answer Thus, the maximum income is 1280.
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Example 1-4a
Check Graph this function on a graphing
calculator, and use the CALC menu to confirm
this solution.
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Example 1-4b
Economics A sports team sells about 100 coupon
books for 30 each during their annual
fund-raiser. They estimate that for each 0.50
decrease in the price, they will sell about 10
more coupon books. a. How much should they charge
for each book in order to maximize the income
from their sales? b. What is the maximum monthly
income the team can expect to make from these
items?
Answer 17.50
Answer 6125