Question

photo necessities produces camera cases. they 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 costs $15.50 to produce 3 camera cases, $23.50 to produce 7 camera cases and $56 to produce 12 cameras.. Complete the function that represents the cost C(x) to produce x camera cases

Answer 1

c(x) = Ax^2 +Bx +C

1) 15.5 = A (3^2) +B(3) + C

15.5 = 9A + 3B + C

2) 23.5 = A(7^2) + B(7) + C

23.5 = 49A + 7B

3) 56 = A(12)^2 + B(12) + C

56 = 144C +12B + C

2) - 1) ==> 8 = 40A +4B ==> 2 = 10A + B ==> B = 2 - 10A

3) - 2) ==> 32.5 = 95A + 5B ==> 6.5 = 19 A + B ==> B = 6.5 - 19A

2 - 10A = 6.5 - 19A

19A -10A = 6.5 - 2
9A = 4.5
A = 4.5/9
A = 0.5

B = 2 - 10A = 2 - 10(0.5) = 2 - 5 = -3

C = 15.5 - 9A - 3B
C = 15.5 - 9(0.5) - 3(-3) = 20

c(x) = Ax^2 + Bx + C

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