Relating The Standard And Factored Forms Worksheet - Chapter 3.2
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113.2
Relating the Standard
and Factored Forms
YOU WILL NEED
GOAL
graph paper
•
Compare the factored form of a quadratic function with its
graphing calculator (optional)
•
standard form.
LEARN ABOUT the Math
Tip
Communication
A company’s revenue is its
To raise money, some students sell T-shirts. Based on last year’s sales,
money earned from sales.
they know that
A revenue function,
R(x),
• they can sell 40 T-shirts a week at $10 each
is the product of the number
• if they raise the price by $1, they will sell one less T-shirt each week
of items sold and price.
5
(number of
Revenue
They picked some prices, estimated the number of shirts they might sell,
items sold)(price)
and calculated the revenue.
Price ($)
T-shirts Sold
Revenue ($)
10 3 40 5 400
10
40
10 1 15 5 25
40 2 15 5 25
25 3 25 5 625
10 1 30 5 40
40 2 30 5 10
40 3 10 5 400
Rachel and Andrew noticed that as they increased the price, the revenue
increased and then decreased. Based on this pattern, they suggested
quadratic functions to model revenue, where x is the number of $1
increases.
R(x) 5 (40 2 x) (10 1 x).
• Rachel’s function is
R(x) 5 2x
1 30x 1 400.
2
• Andrew’s function is
?
What is the maximum revenue they can earn
on T-shirt sales?
132
Chapter 3
NEL
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