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 $61 to produce 3 calculators, and $165 to produce 7 calculators, and $385 to produce 12 calculators. Find the total cost of producing 6 calculators.

Answer 1

Set up a quadratic equation.

It has to be C(x) = Ax^2 + Bx + C our job is to find A, B and C given our statements.
where x is the number of calculators
C(3) = 61 = A(3)^2 + B(3) +C
C(7) = 165 = A(7)^2 + B(7) + C

Find C(12) similarly.

then solve 3 equations in 3 unknowns simultaneously for A, B and C