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 $16 to produce 2 widgets, $18 to produce 4 widgets, and $48 to produce 10 widgets.
Find the total cost of producing 8 widgets.

( you use quadratic function formula)

Answer 1

Any ideas???

Answer 2

@Jamierox4ev3r @bibby @Directrix @Goten77 @mathstudent55 @Firejay5

Answer 3

not at all @pielover123

Answer 4

@GabbyGabsterz @Holly00d1248 @Jamielynne @Michele_Laino @leletoomuch

Answer 5

c(x) = ax^2 + bx + d for some a, b, and d
Substitute (2, 30), (4, 118), and (10, 766) for (x, y):
30 = a(2^2) + b(2) + d
118 = a(4^2) + b(4) + d
766 = a(10^2) + b(10) + d
Now you can solve the system of equations for a, b, and d, which will give you c(x)

Answer 6

Are you lost or do you follow?

Answer 7

and how did you get that @pielover123

Answer 8

Do you know what X=?

Answer 9

8 @pielover123

Answer 10

Total Cost for 8 Widgets = $320

Answer 11

why (2, 30), (4, 118), and (10, 766)? @pielover123

Answer 12

My dad is helping me Honest i just wrote down what he told me to put

Answer 13

cant be 320 becasue it cost 48$ to produce 10 @pielover123

Answer 14

I think this @pielover123 :
16 = a(2^2) + b(2) + d
18 = a(4^2) + b(4) + d
48 = a(10^2) + b(10) + d

Answer 15

your right but once you simply that and put it in the calculator it says no solution which is the part thats confusing me @Michele_Laino

Answer 16

please wait I try to compute your solution @bdfhbfg

Answer 17

alright thanks i just need to find out what a,b,and c would be @Michele_Laino

Answer 18

I got these values:
a= 1/2
b= - 2
d= 18
so your function, is:
\[c(x) = \frac{{{x^2}}}{2} - 2x + 18\]

Answer 19

then your answer is:
\[c\left( 8 \right) = \frac{{{8^2}}}{2} - 2 \cdot 8 + 18 = ...?\]

Answer 20

hold on for a second @Michele_Laino

Answer 21

THANK YOUUUUUUUU YOU LITERALLY SAVED MY GRADE!. @Michele_Laino

Answer 22

thank you! :)

Answer 23

appreciate you man! ! great guy @Michele_Laino

Answer 24

thanks! again!