can anyone help with solving problems using quadratic functions?

- anonymous

can anyone help with solving problems using quadratic functions?

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- chestercat

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- amistre64

perhaps, whatcha need?

- anonymous

The company discovered that it costs $30 to produce 2 widgets, $118 to produce 4 widgets, and $766 to produce 10. Using the quadratic function, find the cost of producing 6 widgets.

- amistre64

when you are given 3 points, you need to do what looks like a reverse quadratic....
lets determine the points for our graph:
(2,30) (4,118) (10,766).. ok?

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## More answers

- amistre64

now we want a curve to match these numbers, so we need to find the "coefficients" of a quadratic equation to solve it...
Ax^2 +Bx +C = y

- amistre64

we know our x's and y's so the ABC becomes our "unknown" variables..backwards I know...

- amistre64

lets form 3 equations and then make them all equal like this:
(2)^2A +(2)B + C = 30
(4)^2A +(4)B + C = 118
(10)^2A +(10)B + C = 766

- amistre64

4a +2b +c = 30
16a + 4b +c = 118
100a +10b +c = 766

- amistre64

lets solve this system of equation :) what yor poison, substitution, elimination, or matrix?

- anonymous

what you mean?

- amistre64

if you dont know what I mean by now, then you are nor ready to solve this.....
a system of equations is where you have 3 equations and want to know where they all have common points.
We do that by either substitution techniques, elimination techniques or a matrix technique

- amistre64

well....2 or more equations with points in common :)

- anonymous

well in the lesson for this assignment it never said anything about any of those.

- amistre64

we could try linear equations, but i gotta tell you, it says to do it with q quadratic....

- anonymous

well the lesson is called "solving equations with quadratic functions"

- amistre64

right, and since they gave you 3 points and no equation, we have to find the equation using those points. We need to solve the 3 equations for a b and c in order to "find" the quadratic equation we need. otherwise, its just a shot in the dark :)

- amistre64

Ill do substitution, it tends to be the most intuative of the methods...takes longer, but is eaiser to follow
4a +2b +c = 30
16a + 4b +c = 118
100a +10b +c = 766

- amistre64

4a +2b +c = 30 solve for "c"
c = -4a -2b + 30 we can use this "value" in the other two equations like this:
16a + 4b +(-4a - 2b +30) = 118
16a -4a +4b -2b = 118 -30

- amistre64

12a +2b = 88
solve for another variable with this:
b = -12a/2 +88/2

- amistre64

use the c "value" in the other equation to get rid of that variable in it like we did to this one:
100a +10b +(-4a -2b +30) = 766
100a -4a +10b -2b = 766 - 30
106a +8b = 736
use the "b" value in this equation to solve for "a"

- amistre64

106a +8(-6a +44) = 736
106a -48a +352 = 736
58a = 384
a = 384/58 ...reduce as needed
we have a solid value for "a" now we can use it to find a solid value for "b"

- amistre64

b = -6(384/58) +44
what does b = ??

- amistre64

b = -1152/29 +44 ..... use this in your a value in your top most equation to find the value for c

- amistre64

and as long as I did my math right, it should give you your a b and c values for your quadratic equation ;)

- amistre64

100-4 is not 106.....

- radar

Would you then substitute 6 in the newly found equation to find the cost of production?

- amistre64

yes you would, and that would give you your answer.

- amistre64

as long as I did all the math right....
106 should be 96
96a -48a +352 = 736
48a = 384
a = 384/48 ...reduce as needed

- amistre64

a = 8...much better ;)

- amistre64

b = -6(8) +44
b = -48 + 44 = -4
a = 8, b = -4

- amistre64

c = -4(8) -2(-4) + 30
c = -32 +8 +30
c = -2+8 = 6
your equation is then:
8x^2 -4x +6

- amistre64

8(6)^2-4(6) +6 = your answer

- amistre64

you can double check the ABC by plugging in t your point information and seeing if it is the same :)

- radar

I think this company is having a heck of a learning curve!

- amistre64

lol ..... the company in the eqample, or openstudy, or racergirlk? :)

- radar

lol whew that was work. cul

- anonymous

Thanks amistre64. would you be willing to help with the 4 i have left?

- amistre64

what!?!?!! ..... maybe later tonight, I have classes in an hour ;)

- anonymous

well thanks for the help

- radar

I substituted the 2, 4, and 10 and obtained the amount of production cost as the problem stated. That is the correct answer, 6 widgets will cost $270, the company would be better off making only 2 widgets per production run!! LOL

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