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October 23, 2014

October 23, 2014

Posted by **John** on Friday, March 22, 2013 at 5:17pm.

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) -
**Reiny**, Friday, March 22, 2013 at 5:26pmYour 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

2nd:

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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