Answer:
c(x) = 2x^2 + 6x + 25
Completed question;
Quick Computing Company produces calculators. They have found that the cost, c(x), of making x calculators is a quadratic function in terms of x. The company also discovered that it costs $45 to produce 2 calculators, $81 to produce 4 calculators, and $285 to produce 10 calculators. Derive the function c(x).
Step-by-step explanation:
Given that;
the cost, c(x), of making x calculators is a quadratic function in terms of x.
c(x) = ax^2 + bx + c
Substituting the 3 case scenarios given;
it costs $45 to produce 2 calculators,
45 = a(2^2) + b(2) + c
45 = 4a + 2b +c .......1
$81 to produce 4 calculators,
81 = a(4^2) + b(4) + c
81 = 16a + 4b + c .......2
and $285 to produce 10 calculators.
285 = a(10^2) + b(10) + c
285 = 100a + 10b + c .......3
Solving the simultaneous equation;
Subtracting equation 1 from 2, we have;
36 = 12a + 2b ......4
Subtracting equation 1 from 3
240 = 96a + 8b .......5
Multiply equation 4 by 4
144 = 48a + 8b ......6
Subtracting equation 6 from 5, we have;
96 = 48a
a = 96/48
a = 2
Substituting a = 2 into equation 4;
36 = 12(2) + 2b
36 = 24 + 2b
2b = 36-24 = 12
b = 12/2 = 6
b = 6
Substituting a and b into equation 1;
45 = 4(2) + 2(6) +c
45 = 8 + 12 + c
c = 45 - (8+12)
c = 25
Since a = 2 , b = 6 and c = 25, the quadratic equation for c(x) is ;
c(x) = ax^2 + bx + c
c(x) = 2x^2 + 6x + 25
