Dear nathan02079,

The quadratic function is the form f(x) = a*x^2 + b*x + c where 'a' not a null.

Now it's

Price(d) = a*d^2 + b*d + c.

We have to find the parameters a, b and c.

We know

Price(8) = 6

Price(12) = 8.5

Price(16) = 11.5

so we know

(1) a*8^2+b*8+c = 6

(2) a*12^2+b*12+c = 8.5

(3) a*16^2+b*16+c = 11.5

[4] (3)-(1) --> 192*a + 8*b = 5.5

[5] (2)-(1) --> 80*a + 4*b = 2.5

[4]-2*[5] --> 32*a = 0.5 --> a = 1/64

[5] --> b = (1/4)*(2.5-80/64) = 5/16

(1) --> c = 6-1-5/2 = 2.5

So

Price(d) = (1/64)*d*d + (5/16)*d + 2.5