Name:___________________________________ #_______
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1. A doorway in a castle is shaped like a parabola. The door is 4 feet across and 8 feet high in the center.
a) Draw a picture and label key points. (x-intercepts, vertex, line of symmetry)
b) Describe a reasonable domain and range.
c) Write an equation in vertex form relating the height to the width of the door.
d) Is the vertex a maximum or a minimum?
e) In regards to the parent function, describe the transformations that were made.
2. The outer door of an airplane hangar is in the shape of a parabola. The door is 120 feet across and 90 feet high.
a) Draw a picture and label key points.
b) Describe a reasonable domain and range.
c) Write an equation in vertex form relating the height of the door to its width.
d) Is the vertex a maximum or a minimum?
e) In regards to the parent function, describe the transformations that were made.
3.. The main cables of a suspension bridge are 20 meters above the road at the towers and 4 meters above the road at
the center. The bridge is 80 meters long. Vertical cables are spaced every 10 meters. The main cables hang in the shape
of a parabola.
a) Draw a picture and label key points.
b) Describe a reasonable domain and range.
c) Write an equation that relates the height of the cables to the length of the bridge.
Cable
Height
d) Is the vertex a maximum or a minimum?
e) Create a table that gives the height of each vertical cable. (See right.)
f) How many cables are 5 meters high? How far are they from the beginning of the bridge?
4. A baseball is thrown from a height of 2 meters and is caught at the same height 40 meters away. During its parabolic
path, it reaches a maximum height of 10 meters.
a) Label the key points on the given picture.
b) Describe a reasonable domain and range.
c) Find the equation which relates the height of the ball to the horizontal distance it has traveled.
d) What is the height of the ball after it has traveled a horizontal distance of 30 meters?
e) If the ball is not caught, at what distance will it strike the ground?
f) At what distances did the ball reach a height of 6 meters? Round to the nearest hundredths.
5. An arrow is shot over a lake from a cliff that is 10 feet above the lake. The arrow returns to the same height as the
cliff at a distance of 150 feet from the cliff. Its path is in the shape of a parabola and reaches a height of 60 feet above
the lake.
a) Label the key points on the given picture.
b) Describe a reasonable domain and range.
c) Write an equation that relates the height of the arrow above the lake to its horizontal distance from the cliff.
Distance
Height
d) Create a table showing the arrow’s height every 25 feet to the nearest hundredths.
e) What is the arrow’s height above the water when it has traveled a horizontal distance of 120 feet?
f) At what distance from the cliff will the arrow strike the lake?
g) As it travels, how many times will the arrow reach a height of 40 feet? Calculate the horizontal distances where this
occurs.
.
6. The shape of the Gateway Arch in St. Louis, Missouri is a catenary curve, which closely resembles a parabola. The
function y = -
2 2
x
315
+ 4x models the shape of the arch, where y is the height in feet and x is the horizontal distance
from the base of the left side of the arch in feet.
a) Graph the function on your calculator and find its vertex and zeros.
b) Label the key points on the given picture.
c) Describe a reasonable domain and range for the function.
d) According to the model, what is the maximum height of the arch?
e) What is the width of the arch at its base?