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McDougal's Restaurant has a play area for children under and around their giant arch ( in the shape of parabola with negative orientation). They plan to set up a new activity that allows children to bungee jump from the arch. The manager, upon hearing of your team's expertise, hires you to calculate the maximum stretch of the rope that will keep the kids safe. The arch is 50 feet high and 40 feet wide at the base. The jumping location will be 5 horizontal feet away from the axis of symmetry of the arch.

A. Write an equation to model the shape of the arch.

  • math -

    let the x-axis be the ground and the y-axis the axis of symmetry
    Make a sketch, your jump will be when x = 5

    equation is y = ax^2 + 50
    but (20,0) is the x-intercept , the other is (-20,0)
    so 0 = a(20^2) + 50
    400a = -50
    a = -1/8

    y = (-1/8)x^2 + 50
    when x = 5
    y = (1/8)(25) + 50 = 46.875 ft

    max stretch is 46.875 ft, (it will "touch" the ground)

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