Hello, I was given a 30-question worksheet on quadratic equation problems. I have about 4 questions I can't solve. I'll post up one for now. Help is greatly appreciated. Thank you!

Pizza Unlimited has the following prices for pizzas.

8 in. - $6 12 in. -$8.50
16 in. - $11.50 Is price a quadratic function of diameter? It probably should be, because the price should be proportional to the area, and the area is a quadratic function of the diameter. (The area of a circular region is given by$\displaystyle A=\pi r^2 or (\pi/4)*d^2.)\$

a) Express price as a quadratic function of diameter using the data points (8,6), (12,8.50), and (16,11.50).

b) Use the function to find the price of a 14-in. pizza.

Thank you!

2. 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