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perhaps, whatcha need?
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.
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?
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
we know our x's and y's so the ABC becomes our "unknown" variables..backwards I know...
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
4a +2b +c = 30 16a + 4b +c = 118 100a +10b +c = 766
lets solve this system of equation :) what yor poison, substitution, elimination, or matrix?
what you mean?
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
well....2 or more equations with points in common :)
well in the lesson for this assignment it never said anything about any of those.
we could try linear equations, but i gotta tell you, it says to do it with q quadratic....
well the lesson is called "solving equations with quadratic functions"
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 :)
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
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
12a +2b = 88 solve for another variable with this: b = -12a/2 +88/2
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"
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"
b = -6(384/58) +44 what does b = ??
b = -1152/29 +44 ..... use this in your a value in your top most equation to find the value for c
and as long as I did my math right, it should give you your a b and c values for your quadratic equation ;)
100-4 is not 106.....
Would you then substitute 6 in the newly found equation to find the cost of production?
yes you would, and that would give you your answer.
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
a = 8...much better ;)
b = -6(8) +44 b = -48 + 44 = -4 a = 8, b = -4
c = -4(8) -2(-4) + 30 c = -32 +8 +30 c = -2+8 = 6 your equation is then: 8x^2 -4x +6
8(6)^2-4(6) +6 = your answer
you can double check the ABC by plugging in t your point information and seeing if it is the same :)
I think this company is having a heck of a learning curve!
lol ..... the company in the eqample, or openstudy, or racergirlk? :)
lol whew that was work. cul
Thanks amistre64. would you be willing to help with the 4 i have left?
what!?!?!! ..... maybe later tonight, I have classes in an hour ;)
well thanks for the help
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