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PSAT 1.37 Math Diagnostic 177 Views


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Description:

PSAT 1.37 Math Diagnostic. Which of the following forms of the function f(x) would best reveal the number of employees that should be hired to maximize points?

Language:
English Language

Transcript

00:00

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

00:05

Brought to you by new employees You can tell which

00:08

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

00:10

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

00:14

be modelled with the function F of x equals negative

00:16

twenty five x squared plus one hundred fifty x minus

00:19

twenty five where ex represents the number of employees which

00:23

of the following forms of the function f effects would

00:25

best reveal the number of employees that should be hired

00:28

to maximize profits And here the potential answers All right

00:32

kind of ugly Okay so this company who shall not

00:35

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

00:39

really flame of companies who focus on minimizing their profit

00:43

tend not to stick around very long or we call

00:45

them of the u s government Okay so we have

00:48

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

00:51

to figure out what form of that function shows how

00:54

many newbies the company should ideally higher if they want

00:57

to crack their way into the fortune five hundred in

00:59

graph form this would be the vertex of the para

01:02

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

01:04

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

01:07

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

01:09

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

01:12

of trying out each option provided to see which one

01:15

a shows the vertex and b is it equivalent to

01:19

the original function now that said we can instantly rule

01:22

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

01:25

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

01:29

find a vertex at all Just been one of you

01:32

Each of the other three answer choices could get us

01:34

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

01:37

him out and see which one is equivalent to our

01:39

function Well option c is why equals negative twenty five

01:43

times the quantity x plus three times the quantity x

01:46

minus two were multiplying the parentheses first we get x

01:49

squared minus two x plus three ex finest six the

01:53

ex terms simplified a positive one x So next we

01:56

have to take negative twenty five and multiplied by each

01:59

of the terms and our new polynomial x squared plus

02:02

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

02:05

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

02:09

match the function so option c can talk to the

02:12

hand What about option d Why equals twenty five times

02:16

the quantity Negative Acts minus 3 times the quantity x

02:19

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

02:23

stuff in parentheses Well that all comes out to negative

02:26

x squared minus two Acts minus 3 x minus 6

02:29

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

02:32

five X minus six Now we bring the twenty five

02:35

into the mix and we get negative Twenty five x

02:37

squared minus one hundred fifty x minus one fifty closer

02:41

but still no salami fingers crossed That answer b works

02:44

out then So we have Why equals negative twenty five

02:48

times quantity x minus three squared plus two hundred For

02:52

starters we can rewrite this so that the stuff in

02:54

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

02:58

means anyway the quantity x minus three times the quantity

03:00

x minus really give us x squared minus three x

03:03

minus three acts plus nine four x squared minus six

03:07

x plus nine which went multiplied by nega twenty five

03:11

gives us negative twenty five x squared plus one hundred

03:14

fifty x minus two hundred twenty five Of course we

03:17

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

03:20

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

03:23

an equation that reads Why equals negative twenty five x

03:26

squared plus one hundred fifty x minus twenty five Bingo

03:29

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

03:32

at Now that the company is maximizing their profits it

03:35

sure would be nice if they invested in a new

03:37

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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