Company abc 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 $23 to produce 2 widgets, $55 to produce 4 widgets, and $247 to produce 10 widgets. what is the total cost of producing 8 widgets?

  C(x) = ax^2 + bx + c since it is quadratic. 
C(2) = 23, C(4) = 55, C(10) = 247. 
Plugging all this in: 
4a + 2b + c = 23 
16a + 4b + c = 55 
100a + 10b + c = 247 

Solving simultaneously: 
6a + b = 16 
14a + b = 32 

a= 2, b = 4, c = 7 

So total cost of producing 8 widgets = 2(8)^2 + 4(8) + 7 
= 128 + 39 = $167