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Math Help - Semi-circle function

  1. #1
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    Semi-circle function

    The graph of y=(3x-x)^.5 is a semi-circle with diameter coincident with the positive x-axis, radius 1.5, center at (1.5,0). create a function passing through (3.5,5) and intersecting the x-axis at x=2 and x=5.
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  2. #2
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    Hello, sjenkins!

    The graph of y=(3x-x)^.5 is a semi-circle with diameter coincident
    with the positive x-axis, radius 1.5, center at (1.5,0).

    . . All this is all true . . . but who needs it ??

    Create a function passing through (3.5, 5) and intersecting the x-axis at x=2 and x=5.
    Make a sketch . . .
    Code:
            |
            |    (3,5)
            |       *
            |
            |
            |
        - - + - * - - - * - -
            |   2       5
    We can see that a parabola will work.

    From the two x-intercepts, we have: . f(x) \:=\:a(x-2)(x-5)

    To pass through \left(\frac{7}{2},\:5\right), we have: . a\left(\frac{7}{2}-2\right)\left(\frac{7}{2} - 5\right) \:=\:5

    . . a\left(\frac{3}{2}\right)\left(-\frac{3}{2}\right) \:=\:5 \quad\Rightarrow\quad -\frac{9}{4}\,a \:=\:5 \quad\Rightarrow\quad a \:=\:-\frac{20}{9}


    Therefore: . f(x) \:=\;-\frac{20}{9}(x-2)(x-5) \quad\Rightarrow\quad\boxed{ f(x) \;=\;-\frac{20}{9}x^2 + \frac{140}{9}x - \frac{200}{9}}

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