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Math

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Can you please help me with a math problem

Suppose the ball was 3.24 feet above ground when it was hit, and that it reached a maximum height of approximately 102.51 feet when it had traveled a ground distance of approximately 214.26 feet. The ball lands after traveling a ground distance of approximately 432 feet.

Find an equation of the form y = C(x-z1)(x-z2) where z1 and z2 are the zeros (or roots) of the quadratic polynomial (or x-intercepts of the graph) and C is a scaling constant that needs to be determined.

Thanks!

  • Math -

    the vertex is at (214.26,102.51)

    So, y = C(x-214.26)^2 + k
    102.51 = C(0)^2 + k
    so, k = 102.51

    y = C(x-214.26)^2 + 102.51
    0 = C(432-214.26)^2 + 102.51
    C = -0.002162

    y = -0.002162(x-214.26)^2 + 102.51

    y = -.002162x^2 + .92646x + 3.25831
    y = -.002162(x+3.4885)(x-432)

  • Math -

    Why are these poor models for a parabola, Where a ball starts a a certain point and then is hit to reach a maximum height (vertex) and then lands at a certain point

    i. y = -0.002x(x - 437.1)
    ii. y = -0.5x + 216x + 3
    iii. y = -0.002x + 0.879x + 3.981
    iv. y = -0.002x + 0.8732x - 3.981

    Thanks!

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