#1**+10 **

Pete Zarilla sells 10 inch pizzas for $4.30, 12 inch pizzas for $5.88, and 14 inch pizzas for $7.78. Assume that the price is a quadratic function of the diameter.

We have this set of equations

a(10)^2 + b(10) + c = 4.30 → 100a + 10b + c = 4.30 (1)

a(12)^2 + b(12) + c = 5.88 → 144a + 12b + c = 5.88 (2)

a(14)^2 + b(14) +c = 7.78 → 196a + 14b + c = 7.78 (3)

Subtract (1) from (2) and (2) from (3) so we have

44a + 2b = 1.58 (4)

52a + 2b = 1.90 (5)

Subtract (4) from (5) and we have that 8a = .32 → a = .04

And using (5), we have 52(.04) +2b = 1.90 → b = -.09

And using (1) we have

100(.04) + 10(-.09) + c = 4.30 → c = 1.2

So, our function is

P(d) = (.04)d^2 - .09d + 1.2

Here's the graph using "x" for d..........https://www.desmos.com/calculator/iuv83m3xfc

The price for a 5 inch pizza is 1.75

And using the graph, a $20 pizza would have a diameter of about 22.84 inches

I believe that the price-intercept being greater than 0 must represent some sort of "fixed charge" of $1.20, regardless of the size ordered.....

CPhill
Jan 23, 2015

#1**+10 **

Best Answer

Pete Zarilla sells 10 inch pizzas for $4.30, 12 inch pizzas for $5.88, and 14 inch pizzas for $7.78. Assume that the price is a quadratic function of the diameter.

We have this set of equations

a(10)^2 + b(10) + c = 4.30 → 100a + 10b + c = 4.30 (1)

a(12)^2 + b(12) + c = 5.88 → 144a + 12b + c = 5.88 (2)

a(14)^2 + b(14) +c = 7.78 → 196a + 14b + c = 7.78 (3)

Subtract (1) from (2) and (2) from (3) so we have

44a + 2b = 1.58 (4)

52a + 2b = 1.90 (5)

Subtract (4) from (5) and we have that 8a = .32 → a = .04

And using (5), we have 52(.04) +2b = 1.90 → b = -.09

And using (1) we have

100(.04) + 10(-.09) + c = 4.30 → c = 1.2

So, our function is

P(d) = (.04)d^2 - .09d + 1.2

Here's the graph using "x" for d..........https://www.desmos.com/calculator/iuv83m3xfc

The price for a 5 inch pizza is 1.75

And using the graph, a $20 pizza would have a diameter of about 22.84 inches

I believe that the price-intercept being greater than 0 must represent some sort of "fixed charge" of $1.20, regardless of the size ordered.....

CPhill
Jan 23, 2015