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(a) Graph $ y = ax^2 $ for $ a = -2, -1, -0.5, 0.…
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Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 Problem 21 Problem 22 Problem 23 Problem 24 Problem 25 Problem 26 Problem 27 Problem 28 Problem 29 Problem 30 Problem 31 Problem 32 Problem 33 Problem 34 Problem 35 Problem 36 Problem 37 Problem 38 Problem 39 Problem 40 Problem 41 Problem 42 Problem 43 Problem 44 Problem 45 Problem 46 Problem 47 Problem 48 Problem 49 Problem 50 Problem 51 Problem 52 Problem 53 Problem 54 Problem 55 Problem 56 Problem 57 Problem 58 Problem 59 Problem 60 Problem 61 Problem 62 Problem 63 Problem 64 Problem 65 Problem 66 Problem 67 Problem 68 Problem 69 Problem 70 Problem 71 Problem 72 Problem 73 Problem 74 Problem 75 Problem 76 Problem 77 Problem 78 Problem 79 Problem 80 Problem 81 Problem 82 Problem 83 Problem 84 Problem 85 Problem 86 Problem 87 Problem 88 Problem 89 Problem 90 Problem 91 Problem 92 Problem 93 Problem 94 Problem 95 Problem 96 Problem 97 Problem 98 Problem 99 Problem 100

Problem 96 Medium Difficulty

The profit $ P $ (in millions of dollars) for a recreational vehicle retailer is modeled by a quadratic function of the form

P = at^2 + bt + c

where $ t $ represents the year. If you were president of the company, which of the models below would you prefer? Explain your reasoning.

(a)$ a $ is positive and $ -b / (2a) \le t $.
(b)$ a $ is positive and $ t \le -b/(2a) $.
(c)$ a $ is negative and $ -b /(2a) \le t $.
(d)$ a $ is negative and $ t \le -b(2a) $.

Answer

a) Prefer
b) Not Prefer
c) Not Prefer
d) Prefer

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Precalculus with Limits

Chapter 2

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Section 1

Quadratic Functions and Models

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Watch More Solved Questions in Chapter 2

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
Problem 60
Problem 61
Problem 62
Problem 63
Problem 64
Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
Problem 70
Problem 71
Problem 72
Problem 73
Problem 74
Problem 75
Problem 76
Problem 77
Problem 78
Problem 79
Problem 80
Problem 81
Problem 82
Problem 83
Problem 84
Problem 85
Problem 86
Problem 87
Problem 88
Problem 89
Problem 90
Problem 91
Problem 92
Problem 93
Problem 94
Problem 95
Problem 96
Problem 97
Problem 98
Problem 99
Problem 100

Video Transcript

Okay, let's consider whether is positive. So remember, this means that travel opens up forward. But if is negative, as in C or D, then other direction. And also you see the significance of negative B over two A. Okay, that's what we call the access of symmetry. And this is the Baroque align. Here are our case. I guess we should say not. Expert t since he is the year so really, In our case, we should just be considering positive t secret Northern Negative Thi s is so this point right here. Negative B over two A and similarly over here is well, so in case one, eh? You see, you want he bigger than they're going to be over too, eh? So negative b over two way that will be the minimum And is if you take teeth as time goes on, years passed by your profit continues to grow and brought a faster rate. So that by itself let me conclude that the answer should be a But let's also consider the other cases in case be a still positive. But now that he's less than the ex corner of the vortex But in this case, your profit will increase as you go left. However, we can go beyond a certain point because tes can go too negative Infinity because represents the year. So you're maximum profit would be bounded in case B. Where is its unbounded in case, eh? And in part C and E In this case, we see that the max profit here is that the Vertex But if you take tea larger or less than the earth takes than your profits and either case decrease and we don't want that so we'll cross off, See? Indeed. So we conclude that the answer is a

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