Question

Widget Wonders produces widgets. They have found that the cost, c(x), of making x widgets is a quadratic function in terms of x.
The company also discovered that it costs $29 to produce 2 widgets, $115 to produce 4 widgets, and $757 to produce 10 widgets.

Complete the function that represents the cost, c(x), to produce x widgets.

Answer 1

Let \(c(x)=ax^2+bx+c\). Put the three sets of value in and solve it.

Answer 2

So,
c(x)=29x^2+115x+757?

Answer 3

No.
The first set of conditions is \(c(2)=27\). Can you fnd the other ones?

Answer 4

c(4)=115?

Answer 5

And the last one?

Answer 6

c(10)=757

Answer 7

Okay, put that back into \(c(x)=dx^2+ex+f\). I changed a, b and c to d, e and f because the function is c and the constant is c too. That is a bit confusing. The first equation would be \(2^2d+2e+f=29\). Just create the three equations and solve it.

Answer 8

So the second one would be 4x^2+4x+c=115?

Answer 9

No. You know that c(4)=115 and \(c(x)=dx^2+ex+f\). You replace all x in c(x) with 4 as you want c(4). That is:
\[
c(4)=d4^2+e4+f=115\\
=16d+4e+f=115\]

Answer 10

@Callisto I am now at Sogo because of the sale and I don't think it is a good idea to do OpenStudy while walking in a crowded area so please help!

Answer 11

Aiya! Sorry for the belated reply. As Thomas has mentioned, since the function is quadratic in x, we have c(x) = ax^2 + bx + c
Also, we are given when 2 widgets are produced, the cost is $29, i.e. c(2) = 29.
When 4 widgets are produced, the cost is $115,i.e. c(4) = 115 and when 10 widgets are produced, the cost is $757, i.e. c(10)=757.
So, we have the system:
29 = (2^2) a + 2b + c
115 = (4^2) a + 4b + c
757 = (10 ^2 ) a + 10b + c
Now, you need to simply the equations and solve the system.

Answer 12

thank you guys so much!!! @callisto @thomas5267