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anonymous
 one year ago
You are having a meeting with the CEO of a technology company. You have interpreted the number of laptops produced versus profit as the function P(x) = x4 3x3 8x2 + 12x + 16. Describe to the CEO what the graph looks like. Use complete sentences, and focus on the end behaviors of the graph and where the company will break even (where P(x) = 0).
anonymous
 one year ago
You are having a meeting with the CEO of a technology company. You have interpreted the number of laptops produced versus profit as the function P(x) = x4 3x3 8x2 + 12x + 16. Describe to the CEO what the graph looks like. Use complete sentences, and focus on the end behaviors of the graph and where the company will break even (where P(x) = 0).

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Let's figure out the end behavior first. Look at the drawing I put up. Which scenario matches your polynomial? http://openstudy.com/users/peachpi#/updates/55e729cee4b0819646d8891a

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what do you think this will look like on the right and left ends?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0look at the leading coefficient and degree of your function. You need to look at whether the degree is odd or even and whether the leading coefficient is positive or negative. There are 4 different options for end behavior based on those.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0would the leading coefficient be x4? @peachpi

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and i'm not sure what the graph would look like @peachpi

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0sorry. I stepped away for a moment. The degree is the highest exponent. That's 4. The leading coefficient is the number in front of \(x^4\). There's no number actually written, so the leading coefficient is 1.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That means you have an EVEN DEGREE polynomial with a POSITIVE LEADING COEFFICIENT.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohhh that does make sense @peachpi

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok, so now that we have that info, what will the ends of your graph look like? If you look at that drawing there are 4 options based on degree and leading coefficient both ends up both ends down left end up, right end down left end down, right end up

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i think the left and the right would be up

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Exactly. So as part of your answer you'd say both ends of the graph go up because the degree is even and the leading coefficient is positive.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Now we can solve the equation to find the breakeven point. \[x^43x^38x^2+12x+16=0\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0alright. do you know synthetic division?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0im not the best at it though

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok. I was trying to factor, but I don't think that will work. Unfortunately it looks like we have to divide. Basically any real roots have to be factors of 16. So typically you have to try a bunch of them and see which works. I've already tried 4 and it works, so we have this.dw:1441291472156:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So now it's \[(x4)(x^3+x^24x4)=0\] The second part of that can be factored by grouping \[(x4)[x^2(x+1)4(x+1)]=0\] \[(x4)(x+1)(x^24)=0\] Then factor the difference of squares \[(x4)(x+1)(x+2)(x2)=0\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah sorry im writing some of this down

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no problem. let me know when you're ready

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok im ready now @peachpi

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok so we know the zeros are 4, 1, 2, and 2. Plot them on the xaxis. (please pardon my sorry excuse for points)dw:1441292680506:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0This is where the end behavior comes in. We know that the graph goes up on both ends, so we can do thisdw:1441292840024:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohhh wow i actually understand this now :D

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0:) cool. Now we just need to make a reasonable guess at the middle.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0basically, (anytime you don't have repeated roots), a polynomial will switch sides of the xaxis when it passes through a zero. So since it's positive to the left of 2, it will be negative between 2 and 1. Then positive again, then negative, then finally positive where we have the right end drawn dw:1441293088769:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It's really hard to draw a smooth curve on this, so plot it on https://www.desmos.com/calculator to see what it really looks like

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The only other thing I think you can do is say the yintercept is 16dw:1441293360697:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what would the end behaviors be ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The end behavior is both ends of the graph go up because the degree is even and the leading coefficient is positive. The yintercept is 16 so the profit was $16 when 0 laptops were produced. Then profit increases to a local maximum between 0 and 2 produced. Then the company loses money between 2 and 4 produced before breaking even permanently at 4 produced.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thank you so much i seriously appreciate all you've helped me with
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