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zloy xaker [14]
3 years ago
10

PLEASE HELP!!! Find a quadratic model for the set of values: (-2, -20), (0, -4), (4, -20). Show your work.

Mathematics
1 answer:
Mice21 [21]3 years ago
3 0
Alright

so we have a set of points

any quadratic function can be represeted by the form
y=ax²+bx+c
where a, b, and c are all constants
sometimes we use f(x) instead of y

anyway

we can find the values of a, b, and c by subsituting the points


ok
for (-2,-20)
x=-2 and y=-20
-20=a(-2)²+b(-2)+c or
-20=4a-2b+c

for (0,-4)
x=0 and y=-4
-4=a(0)²+b(0)+c
-4=c
neato
we can subsitute -4 for c later to find a and b later

using (4,-20)
x=4 and y=-20
(at this point we notice that (-2,-20) and (4,-20) have same y values so the x value of the vertex will be the midpoint of the 2 x values which is at x=1 and we can do math to find the other things but whatever)
x=4 and y=-20
-20=a(4)²+b(4)+c
-20=16a+4b+c


alright

we've got
-20=4a-2b+c
-4=c
-20=16a+4b+c

usinb -4=c
-20=4a-2b-4
-20=16a+4b-4
add 4 to everybody
-16=4a-2b
-16=16a+4b
elimination

multiply top equation by 2 and add to 2nd equation
-32=8a-4b
-16=16a+4b +
-48=24a+0b

-48=24a
divide both sides by 24
-2=a
sub back into one of the equations
-16=4a-2b
-16=4(-2)-2b
-16=-8-2b
add 8
-8=-2b
divide by -2 both sides
4=b

a=-2
b=4
c=-4

y=-2x²+4x-4
or
f(x)=-2x²+4x-4
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Answer:

Assuming you want better payment each week, any number of hours above 33.333 or 33 hours and 20 minutes per week

Step-by-step explanation:

There are several ways we could do this.  We could say we want to have Tim Hortons be the better employer on the first week, or after so many weeks by adjusting the hours.  I am going to assume we are saying we want it to be a better employer on the first week, so the profit will be the amount made every week plus the money made per hour times the number of hours.

Let's say number of hours is H

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If you set the two expressions equal to each other you will find where they intersect, which means at that number of hours they will give the same amount of money while any amount before one of the companies will give more and after that many hours the other will.  Let's go ahead and solve.

200 + 5H = 300 + 2H

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H = 100/3

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200 + 5(33.333) = 366.665 which rounds to 366.67 dollars

300 + 2(33.333) = 366.666 which also rounds to 366.67 dollars

So at 33.333 hours both give 366.67 dollars.  Let's look at a value below it, say 32.

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So you can see here Tim Hortons  pays less.  Now we will try 34 as a value above 33.333

200 + 5(32) = 370

300 + 2(32) = 368

Here Mcdonalds pays less.  This was to show that values below 33.333 make Tim Hortonspay less and values above 33.333 make Mcdonalds pay less.  In other words any value above 33.333 hours will have Tim Hortons be the better employer.  And this is per week

I want to repeat, you can expand this to be multiple weeks and see which of the two becomes better in that epriod of time.  This was, I think, the simplest way to answer though.  

So the conditions where Tim Horton pays more isif you work more than 33.333 hours per week.  This will make them pay more every single week.  

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