Grade 11 Functions

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A baseball player hits a foul ball into the stands. He wants to know where the ball would've landed if the stands had not been there. The points they give you are: The y-intercept (0,1), (2,2.5) and (134,18). I'm pretty sure you are looking for the zeroes.

  • Grade 11 Functions -

    assuming the ball's trajectory to be a parabola,

    y = ax^2 + bx + c

    Plug in the three points and solve for y=0, because that;'s how high the ball would have been when it hit the ground.

    1 = a*0 + b*0 + c
    so, c=1

    y = ax^2 + bx + 1
    2.5 = 4a + 2b
    18 = 17956a + 134b

    multiply the first by 67 and subtract from the second, and we have
    a = -0.00845
    b = 1.2669

    s, we have

    y = -.00845x^2 + 1.2669x + 1
    When y=0, x = 150.714

    Must have hit into the stands about halfway to the outfield fence.

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