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Math Help - Finding a quadratic function based on the graph

  1. #1
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    Finding a quadratic function based on the graph

    Hello,

    I have a problem in a homework assignment that's asking me to take the graph of a quadratic function and write a quadratic function that fits the graph. I thought this would be more straightforward but I'm finding myself stumped.

    The zeros of the graph are (0,0) and (10,0) and the vertex is (5,8). How would I use this information to write a quadratic function?

    Thanks very much in advance.
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  2. #2
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    Quote Originally Posted by paradise737 View Post
    Hello,

    I have a problem in a homework assignment that's asking me to take the graph of a quadratic function and write a quadratic function that fits the graph. I thought this would be more straightforward but I'm finding myself stumped.

    The zeros of the graph are (0,0) and (10,0) and the vertex is (5,8). How would I use this information to write a quadratic function?

    Thanks very much in advance.
    since x = 0 and x = 10 are roots of the quadratic ...

    y = kx(x-10)

    now use the fact that y = 8 when x = 5 to solve for the constant k.
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  3. #3
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    Hi, thanks for the post.

    solving for "k":

    8 = k(5)(5-10)
    8 = k (5) (-5)
    8 = k (-25)
    8 = -25k

    k = -.32

    But...now what?

    y = (-.32)x^2 + bx + c

    ?
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  4. #4
    Super Member Bacterius's Avatar
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    Well, as Skeeter said, that means that your curve can be modelled by the equation :

    y = 0.32x(x - 10)

    By expanding :

    y = 0.32x^2 - 3.2x

    (there is no constant c for this quadratic)
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