Question 728278: Pete sells 10 inch pizzas for $4.30, 12-inch for $5.88, and 14-inch pizzas for $7.78. Assume that the price is a quadratic function of the diameter.
a) write the particular equation expressing price in terms of diameter.
b) predict the price of 5-inch mini pizza
c)If a pizza sells for $20.00 what would expect its diameter to be? (Round to nearest 10th)
d)What is the significance of the fact that the price intercept is greater than zero? (suggest what it might represent)
Answer by josgarithmetic(39618)   (Show Source):
You can put this solution on YOUR website! Writing three quadratic equations using the data and using the general form quadratic coefficients a, b, c, as the variables, you can find that :
a=0.04
b=-0.09
c=1.2
You can use the matrix tool on the Purdue university site (easy to find using a google web search) for help in finding the coefficients. The general form function, if quadratic would be  .
You can Complete the square using the term (9/8)^2, and you can obtain standard form for the function as  . That last constant, 1.15 is approximate, good to three significant figures.
The vertex would be x=9/8, and y=1.15. That is  inch diameter pizza for $1.15. That sort of pizza is probably not practical; but anyway, the minimum being the vertex is ABOVE the horizontal axis, so the function has NO REAL ZEROS.
Using this same equation or function, either or  , just substitute x=5 and evaluate y, to see the price for the 5 inch diameter pizza.
If you want x for y=20, the $20 pizza, you might try taking the standard form of the function you found, and then solve this for x.
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