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.

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