Widget Wonders produces widgets. they have found that the cost, C(X), of making x wigets is a quadratic function in terms of x. the company also discovers that it costs $23 to produce 2 widgets, $103 to produce 4 widgets, and $631 to produce 10 widgets. find the total cost of producing 6 widgets.

Question

Widget Wonders produces widgets. they have found that the cost, C(X), of making x wigets is a quadratic function in terms of x. the company also discovers that it costs $23 to produce 2 widgets, $103 to produce 4 widgets, and $631 to produce 10 widgets.  find the total cost of producing 6 widgets.

driftracer305 · Answer

ok i think i got it......but it's a long process..... u ready?

anonymous · Answer

yes please

driftracer305 · Answer

k...since they have it as quadratic functions....it will be as such:--
f(x) = ax^2 + bx + c
f(2) = 23 = 4a + 2b + c
f(4) = 103 = 16a + 8b + c
f(10) = 631 = 100a + 10b + c

so u have 3 unknowns to solve for....

anonymous · Answer

okay and how do solve them, sorry im stupid at math

jim_thompson5910 · Answer

The second equation should be

f(4) = 103 = 16a + 4b + c

jim_thompson5910 · Answer

Are you allowed to use a calculator?

driftracer305 · Answer

yea  ...... @jim_thompson5910 ......  i stand corrected...... thx....  wait @angelbaby.....  it's long for me as well

anonymous · Answer

yes

anonymous · Answer

@jim_thompson5910

jim_thompson5910 · Answer

oh my bad, I know what's going on. I meant to say (10,631) and not (6,631)

sorry about that

anonymous · Answer

okay

jim_thompson5910 · Answer

change the last point by double clicking on it

you will be able to edit the point

jim_thompson5910 · Answer

change the first 6 to a 10, then hit enter

jim_thompson5910 · Answer

tell me what f(x) changes into

anonymous · Answer

f(x)=6x^2+4x-9

jim_thompson5910 · Answer

I'm getting the same

jim_thompson5910 · Answer

now in the input bar, type  

f(6)

and hit enter

jim_thompson5910 · Answer

the value that pops up is ???

anonymous · Answer

a=236

anonymous · Answer

231 sorry

jim_thompson5910 · Answer

hmm oh ok, yeah 231

jim_thompson5910 · Answer

so that's the total cost to produce 6 units

anonymous · Answer

i have 4 more like this to go ugh

jim_thompson5910 · Answer

doing this problem by hand would mean you'd have to solve a system of equations (or use matrix math). Both definitely ugly

geogebra definitely simplifies things

anonymous · Answer

its saying its incorrect

jim_thompson5910 · Answer

can you show me what it's saying?

anonymous · Answer

attachment

jim_thompson5910 · Answer

i see, the numbers are different from what is shown at the very top of the page

jim_thompson5910 · Answer

your new points are

(2,16)
(4,18)
(10,48)

jim_thompson5910 · Answer

same idea and you're still looking for f(6)

jim_thompson5910 · Answer

so all you have to do is change those 3 points

anonymous · Answer

thats a different equation , im sorry .i havent slept in 3 days so i cant process right now

jim_thompson5910 · Answer

that's ok, maybe getting a bit of sleep will help

anonymous · Answer

i cant sleep till its done these are my last 5 then im finished with the unit'

jim_thompson5910 · Answer

alright

anonymous · Answer

so basically if its for example 3 widgits for $15 its 3,15

jim_thompson5910 · Answer

correct, the point (3,15)

anonymous · Answer

okay i get it now, thank you so much

jim_thompson5910 · Answer

you're welcome

anonymous · Answer

what about this one?

anonymous · Answer

what would the cords be?

jim_thompson5910 · Answer

x is the time
y is the height


1 second, 58 ft ---> (1,58)
2 seconds, 112 ft ---> (2,112)

it starts on the ground at 0 seconds ---> (0,0)


The three points are 
(0,0)
(1,58)
(2,112)

anonymous · Answer

thanks you

jim_thompson5910 · Answer

you're welcome

anonymous · Answer

do i do the same with this one like i did with the last?

jim_thompson5910 · Answer

yes the projectile motion of the canon ball is a parabola (modeled by a quadratic equation)

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