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

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1Name ____________________________________________MATH 2040Test 1 Part 2Spring, 20181.Write an equation in vertex form for the graph below(𝑦𝑦=𝑎𝑎(𝑥𝑥 − ℎ)2+𝑘𝑘), where𝑎𝑎= 1𝑜𝑜𝑜𝑜𝑎𝑎=1,𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑘𝑘𝑎𝑎𝑜𝑜𝑎𝑎𝑖𝑖𝑎𝑎𝑖𝑖𝑎𝑎𝑖𝑖𝑎𝑎𝑜𝑜𝑖𝑖Each 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.25𝑥𝑥 − 𝑥𝑥2= 0.______________________________________________________________________________________3.The marketing research department of a company that manufactures and sells notebook computers hasdetermined the following revenue and cost functions:𝑹𝑹(𝒙𝒙) =𝒙𝒙(𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐 − 𝟔𝟔𝟐𝟐𝒙𝒙)𝑎𝑎𝑎𝑎𝑎𝑎𝑪𝑪(𝒙𝒙) =𝟒𝟒𝟐𝟐𝟐𝟐𝟐𝟐+𝟓𝟓𝟐𝟐𝟐𝟐𝒙𝒙𝑤𝑤ℎ𝑎𝑎𝑜𝑜𝑎𝑎𝑏𝑏𝑜𝑜𝑖𝑖ℎ𝑓𝑓𝑓𝑓𝑎𝑎𝑓𝑓𝑖𝑖𝑖𝑖𝑜𝑜𝑎𝑎𝑖𝑖ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑜𝑜𝑑𝑑𝑎𝑎𝑖𝑖𝑎𝑎𝑜𝑜𝑓𝑓0≤ 𝑥𝑥 ≤40Use 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)?

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Term
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Tags
pH, Decimal, Natural logarithm, Logarithm