Let x = the number of widgets, a, b and c constant and c(x) = total price.
Then:
c(x) = ax² + bx + c (this is the standard form of a quadratic function.
(1) 23 = a(2²) + b(2) + c ↔ 4a + 2b + c = 23
(2) 103 = a(4²) + b(4) + c ↔16a + 4b + c = 103
(3) 631 = a(10²) + b(10) + c ↔100a + 10b + c = 631
We have a system of 3 equations with 3 variables. Solving for a, b, and c
gives:
a=6
b=4
c= - 9
Hence te quadratic equation is : c(x) = 6x² +4x -9
To find the cost of 6 widgets, just repace x by 6
c(6) b= 6(6²) +4(6) -9
c(6) = 216 + 24 - 9
and c(6 widgets) = $231