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Algebra (word problems)

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Studying help!

Flights of leaping animals typically have parabolic paths. The figure illustrates a frog jump superimposed on a coordinate plane. The length of the leap is 9 feet, and the maximum height off the ground is 3a feet. Find a standard equation for the path of the frog. Assume a = 1.

A doorway has the shape of a parabolic arch and is 16 feet high at the center and 8 feet wide at the base. If a rectangular box 7 feet high must fit through the doorway, what is the maximum width the box can have?

  • Algebra (word problems) -

    Your value of a should be -1 , or else your frog would jump up into space.

    Assuming he starts at the origin, (I don't have your diagram), the equation would be
    height = -(x -4.5)^2 + 3


    I am going to place the centre of the doorway at (0,0)
    so the equation is
    y = ax^2 + 16
    but (4,0) lies on it
    0 = a(16) + 16
    a = -1

    y = -x^2 + 16 is the equation of the arch.
    so when y = 7
    7 = -x^2 + 16
    x^2 = 9
    x = ± 3
    the box would be 6 feet wide.

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