The Fosbury Flop Equation (AnswerKey)
The Fosbury Flop changed the sport of high jump and has led to incredible jumping heights. The
current record is 2.45 meters (just over 8 feet!). Suppose you want to beat this record by jumping
over a horizontal bar 2.5 meters high. Your jumping point is 1 meter away from a point directly below
the horizontal bar, but in order to clear the horizontal bar you must be .1 meters above it.
To accomplish the jump you must use the equation of a parabola. Work through the questions below
to develop a model for the path of your jump; then sketch a graph of the parabola.
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Assume the highest point of your parabolic jump is where you pass over the horizontal bar,
what ordered pair gives the location of the vertex? ____(2, 2.6)________________________
What is the equation of your axis of symmetry? _______x=2__________________________
Where are your x-intercepts (zeroes)? ______________x=1 and x=3___________________
Assume the focus of your parabolic jump is on the horizontal bar, what are its coordinates?
____________________________________________(2, 2.5)________________________
Write the equation of the directrix of your parabolic jump. __y=2.7_____________________
What is the equation that models your parabolic jump as your soar past the record?
______________________y=-2.5(x-2)2 + 2.6____________________________________
New record!
Horizontal bar
0.5 m
Jumping point
0.5 m
Practice Questions:
What is the distance p for a parabola that has a vertex at (4, 8) and focus at (4, 12)?
p = 12 - 8 = 4
What is the distance p for a parabola that has a vertex at (-3, 9) and a directrix at y = 6?
p=9-6=3
What is the distance p for a parabola that has a focus at (4, 10) and a directrix at y = 4?
2p = 10 - 4 = 6, so p = 6/2 = 3
Write the equation for the parabola that has a focus at (4, 6) and a directrix at y = 3.
2p = 6 - 3 = 3, so p = 3/2 = 1.5
Vertex: (4, 4.5)
y= (1/6) (x - 4)2 + 4.5
Write the equation for the parabola that has a focus at (18, 4) and a directrix at y = 10.
2p= 10 – 4 = 6, so p = 6/2 = 3
Vertex: (18, 7)
y = (-1/12) (x – 18)2 + 7