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 cost $15.50 to produce 3 widgets, $23.50 to produce 7 widgets, and $56 to produce 12 widgets.
find the total cost of producing 5 widgets.

I know this is an older question, but for those who may come across this question, this is the answer I got.

The answer is $17.5.

Step-by-step explanation:

c(x) = ax^(2) + bx + c

c(3) = 15.5 = (equation)

c(7) = 23.5 = (equation)

c(12) = 56 = (equation)

The first two equations

9a + 3b + c = 15.5      | x -1

+ 49a + 7b + c = 23.5

-9a - 3b - c =-15.5

+ 49a + 7b + c = 23.5

= 40a + 4b = 8/4

= 10a + b = 2

The second and third equations

49a + 7b + c = 23.5     | x -1

+ 144a + 12b + c = 56

-49a - 7b - c = -23.5

+ 144a + 12b + c = 56

= 95a + 5b = 32.5/5

= 19a + b = 6.5

Now, we solve for a, b, and c

10a + b = 2    | x -1

+ 19a + b = 6.5

-10a - b = -2

+ 19a + b = 6.5

= 9a = 4.5/9

= a = 0.5

10(0.5) + b = 2

5 + b = 2    | -5

= b = -3

49(0.5) + 7(-3) + c = 23.5

24.5 - 21 + c = 23.5

3.5 + c = 23.5     | -3.5

c = 20

Then, plug it into the equation

c(x) = 0.5x^2 - 3x + 20

c(x) = 0.5(5)^2 - 3(5) + 20

c(x) = 12.5 - 15 + 20

c(x) = 17.5

c. 4 1/4 pounds