Algebra (word problems)
posted by John .
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?

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
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.