Question

can anyone help with solving problems using quadratic functions?

Answer 1

perhaps, whatcha need?

Answer 2

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.

Answer 3

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?

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

4a +2b +c = 30

16a + 4b +c = 118

100a +10b +c = 766

Answer 8

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

Answer 9

what you mean?

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

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 :)

Answer 16

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

Answer 17

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

Answer 18

12a +2b = 88

solve for another variable with this:

b = -12a/2 +88/2

Answer 19

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"

Answer 20

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"

Answer 21

b = -6(384/58) +44

what does b = ??

Answer 22

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

Answer 23

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

Answer 24

100-4 is not 106.....

Answer 25

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

Answer 26

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

Answer 27

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

Answer 28

a = 8...much better ;)

Answer 29

b = -6(8) +44

b = -48 + 44 = -4

a = 8, b = -4

Answer 30

c = -4(8) -2(-4) + 30

c = -32 +8 +30

c = -2+8 = 6

your equation is then:

8x^2 -4x +6

Answer 31

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

Answer 32

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

Answer 33

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

Answer 34

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

Answer 35

lol whew that was work. cul

Answer 36

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

Answer 37

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

Answer 38

well thanks for the help

Answer 39

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