ShmoopTube

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Thank you We sneak then here's your shmoop du jour

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Brought to you by new employees You can tell which

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ones aren't going to work out the minute you take

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off the training wheels All right the company's profits can

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be modelled with the function F of x equals negative

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twenty five x squared plus one hundred fifty x minus

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twenty five where ex represents the number of employees which

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of the following forms of the function f effects would

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best reveal the number of employees that should be hired

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to maximize profits And here the potential answers All right

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kind of ugly Okay so this company who shall not

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be named is interested in maximizing their profit We can't

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really flame of companies who focus on minimizing their profit

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tend not to stick around very long or we call

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them of the u s government Okay so we have

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a function that models the company's profits and we want

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to figure out what form of that function shows how

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many newbies the company should ideally higher if they want

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to crack their way into the fortune five hundred in

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graph form this would be the vertex of the para

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Villa when we're trying to find a vertex it's always

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a matter of completing the square which we don't have

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to do from scratch here is we've already got a

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few answer choices it's simply going to be a matter

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of trying out each option provided to see which one

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a shows the vertex and b is it equivalent to

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the original function now that said we can instantly rule

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out option a it's equivalent to the original function because

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it is the original function Exactly that doesn't help us

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find a vertex at all Just been one of you

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Each of the other three answer choices could get us

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to a possible over attacks so we'll need to multiply

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him out and see which one is equivalent to our

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function Well option c is why equals negative twenty five

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times the quantity x plus three times the quantity x

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minus two were multiplying the parentheses first we get x

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squared minus two x plus three ex finest six the

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ex terms simplified a positive one x So next we

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have to take negative twenty five and multiplied by each

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of the terms and our new polynomial x squared plus

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x minus six Now don't give us negative twenty five

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x squared minus twenty five Acts plus 1:500 nuts doesn't

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match the function so option c can talk to the

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hand What about option d Why equals twenty five times

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the quantity Negative Acts minus 3 times the quantity x

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plus two Well same deal as before Let's distribute this

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stuff in parentheses Well that all comes out to negative

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x squared minus two Acts minus 3 x minus 6

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For once we've combined like terms negative x squared minus

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five X minus six Now we bring the twenty five

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into the mix and we get negative Twenty five x

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squared minus one hundred fifty x minus one fifty closer

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but still no salami fingers crossed That answer b works

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out then So we have Why equals negative twenty five

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times quantity x minus three squared plus two hundred For

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starters we can rewrite this so that the stuff in

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parentheses is multiplied by itself Since that's what the experiment

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means anyway the quantity x minus three times the quantity

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x minus really give us x squared minus three x

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minus three acts plus nine four x squared minus six

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x plus nine which went multiplied by nega twenty five

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gives us negative twenty five x squared plus one hundred

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fifty x minus two hundred twenty five Of course we

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can't forget to add that extra two hundred that's tacked

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onto the end And once we've done that we have

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an equation that reads Why equals negative twenty five x

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squared plus one hundred fifty x minus twenty five Bingo

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that's our original function and option b is where it's

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at Now that the company is maximizing their profits it

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sure would be nice if they invested in a new

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copy machine The last fifteen years It's just been some 00:03:40.578 --> [endTime] guy named bob and a boatload of carbon paper

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