MATH 2040 Test 1 Part 2 - Spring 2018 2 .pdf - Name MATH...

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Name ____________________________________________ MATH 2040 Test 1 Part 2 Spring, 2018
1. Write an equation in vertex form for the graph below ( 𝑦𝑦 = 𝑎𝑎 ( 𝑥𝑥 − ℎ )
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+ 𝑘𝑘 ) , where
𝑎𝑎 = 1 𝑜𝑜𝑜𝑜 𝑎𝑎 = − 1, 𝑎𝑎𝑎𝑎𝑎𝑎 ℎ 𝑎𝑎𝑎𝑎𝑎𝑎 𝑘𝑘 𝑎𝑎𝑜𝑜𝑎𝑎 𝑖𝑖𝑎𝑎𝑖𝑖𝑎𝑎𝑖𝑖𝑎𝑎𝑜𝑜𝑖𝑖
Each tick mark represents one unit, so the window is -7 < x < 2 and -10 < y < 2.
The equation in vertex form is y = ____________________________________
The coordinates of the vertex are ____________________________________
The vertex is a minimum or a maximum? ______________________________
The range of the function written as an inequality or in interval notation is: ________________________
2. Use you graphing calculator to find the solution of the following equation, rounded to two decimal places.
2 − 5 𝑥𝑥 − 𝑥𝑥
2
= 0
.
______________________________________________________________________________________
3. The marketing research department of a company that manufactures and sells notebook computers has
determined the following revenue and cost functions:
𝑹𝑹 ( 𝒙𝒙 ) = 𝒙𝒙 ( 𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐 − 𝟔𝟔𝟐𝟐𝒙𝒙 ) 𝑎𝑎𝑎𝑎𝑎𝑎 𝑪𝑪 ( 𝒙𝒙 ) = 𝟒𝟒𝟐𝟐𝟐𝟐𝟐𝟐 + 𝟓𝟓𝟐𝟐𝟐𝟐𝒙𝒙 𝑤𝑤ℎ𝑎𝑎𝑜𝑜𝑎𝑎 𝑏𝑏𝑜𝑜𝑖𝑖ℎ 𝑓𝑓𝑓𝑓𝑎𝑎𝑓𝑓𝑖𝑖𝑖𝑖𝑜𝑜𝑎𝑎𝑖𝑖 ℎ𝑎𝑎𝑎𝑎𝑎𝑎 𝑎𝑎 𝑎𝑎𝑜𝑜𝑑𝑑𝑎𝑎𝑖𝑖𝑎𝑎 𝑜𝑜𝑓𝑓 0 ≤ 𝑥𝑥 ≤ 40
Use a y-window from 0 – 25,000.
a. Find the break-even points. How many computers must be made for the company to break-even?___________
b. Find the profit function P(x). Write the function in simplified form. P(x) = _______________________________
c. Using your calculator, find the maximum profit. ______________________________
d. How many computers must be sold to make the maximum profit? ________________________
e. What is the relationship between the break-even points and the x-intercepts of P(x)?