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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) $.

a) Preferb) Not Preferc) Not Preferd) Prefer

Algebra

Chapter 2

Polynomial and Rational Functions

Section 1

Quadratic Functions and Models

Quadratic Functions

Complex Numbers

Polynomials

Rational Functions

Missouri State University

McMaster University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

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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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