Finding the Quadratic function for price, given diameter

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jshaziza

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Jan 26, 2007
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Pizza Unlimited has the following prices for pizzas.

Diameter Price
8 inches $ 6.00
12 inches $ 8.50
16 inches $ 11.50

The price is a quadratic function based on the diameter of the pizza.
a. Express price as a quadratic function of diameter using the data given.

b. Use the functio from a. above to find the price of a 14-inch pizza.

I used the formula D(x)=ax^2 +bx+c to solve this function.
6=a(8)^2+b(8)+c
8.5=a(12)^2+b(12)+c
11.5=a(16)^2+b(16)+c

Where I got stuck, was when I was using the elimination method to solve for the formulas, I was only able to get rid of one variable and then I was stuck with the other two. If somoeone could show me what I did wrong that would be great. Thx.
 
Re: Finding the Quadratic function

jshaziza said:
Pizza Unlimited has the following prices for pizzas.

Diameter Price
8 inches $ 6.00
12 inches $ 8.50
16 inches $ 11.50

The price is a quadratic function based on the diameter of the pizza.
a. Express price as a quadratic function of diameter using the data given.

b. Use the functio from a. above to find the price of a 14-inch pizza.

I used the formula D(x)=ax^2 +bx+c to solve this function.
6=a(8)^2+b(8)+c
8.5=a(12)^2+b(12)+c
11.5=a(16)^2+b(16)+c

Where I got stuck, was when I was using the elimination method to solve for the formulas, I was only able to get rid of one variable and then I was stuck with the other two. If somoeone could show me what I did wrong that would be great. Thx.
Click to expand...
Please show the steps you took to eliminate - so that we can explain your mistake (if any).
 
SK I took the first and second formulas and multiplied them by 3 and -2 to get rid of b, but my problem would be on how to get rid of c so I can solve for a. Thx for your help.
 
I think you should make the elimination of "c" your FIRST step.

Multiply equation (1) by -1. Add this to both equation (2) and equation (3). That will leave you with two equations containing only "a" and "b".....then you can work on eliminating one of them.
 
jshaziza said:
Pizza Unlimited has the following prices for pizzas.
Code: 
                   Diameter              Price
                    8 inches               $ 6.00
                   12 inches              $  8.50
                   16 inches              $ 11.50
The price is a quadratic function based on the diameter of the pizza.
a. Express price as a quadratic function of diameter using the data given.

b. Use the functio from a. above to find the price of a 14-inch pizza.

I used the formula D(x)=ax^2 +bx+c to solve this function.
6=a(8)^2+b(8)+c...............................(1)
8.5=a(12)^2+b(12)+c.........................(2)
11.5=a(16)^2+b(16)+c.......................(3)

Where I got stuck, was when I was using the elimination method to solve for the formulas, I was only able to get rid of one variable and then I was stuck with the other two. If somoeone could show me what I did wrong that would be great. Thx.
Click to expand...

Subtract (1) from (2)

80a + 4b = 2.5 .................................................(4)

Subtract (2) from (3)

112a + 4b = 3.5 .................................................(5)

Subtract (4) from (5)

32 a = 1.......................................................................(6)

a = 1/32

Using (6) in (4)

4b = 2.5 - 80/32 = 0

b = 0..............................................................(7)

Use (6) and (7) in (1)

c = 6 - 2 = 4
 
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