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The sluggers were up to bat in the bottom of 9 th inning.theo slam was up to bat. As he hit the ball toward left field, it rose from 3 to 10 to 50 feet as the horizontal distance from home plate increased from 0 to 2 to 14 feet. Assume that the vertical distance varies quadratic ally with the horizontal distance. Define variable,write the ordered pairs and find the equation. What is the highest point the ball obtains? Will the ball make it over a 6 foot fence 295 feet from home plate.

  • Math -

    y = k x^2 + b x + c

    x , y
    (0 ,3 )
    (2 , 10 )
    (14, 50 )

    3 = k (0)^2 + b (0) + c
    10 = k(2)^2 + b (2) + c
    50 = k (14)^2 + b (14) + c
    so
    c = 3
    7 = 4 k + 2 b
    47 = 196 k + 14 b

    49 = 28 k + 14 b
    47 = 196 k + 14 b
    -------------------subtract
    2 = - 168 k
    k = - .0119
    then
    7 = 4(-.0119) + 2 b
    b = 3.523
    so
    y = -.0119 x^2 + 3.523
    You can take it from there. Find the vertex by completing the square uness you know calculus, then find y at x = 295

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