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Math Help - Quadratic Functions

  1. #1
    Junior Member
    Joined
    Oct 2007
    Posts
    68

    Arrow Quadratic Functions

    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 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!
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  2. #2
    Member
    Joined
    Dec 2008
    Posts
    111
    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
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