Photo necessities produces camera cases. they have found that the cost , c (x) of making x camera cases is a quadratic function in terms of x. the company also discovered that it cost $45 to produce 3 camera cases $257 to produce 7 camera cases and $792 to produce 12 camera cases. find the total cost producing 1 camera case

The first thing you should know is that to define a quadratic function you need three points.
 In this case the points will be:
 (3. 4. 5)
 (7, 257)
 (12, 792)
 The equation of the quadratic function in this case will be:
 c (x) = 6x ^ 2 - 7x + 12
 Therefore for x = 1 we have:
 c (1) = 6 * (1) ^ 2 - 7 * (1) + 12
 c (1) = 11 $
 
 Total cost producing 1 camera case is:
 c (1) = 11 $