Algebraic equations functions and graphing questions

Algebraic equations/functions and graphing questions, would be best to use grid paper, there are 3 tasks, clear and logical responses please!
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Fireworks Display Portfolio
ALGEBRA 2 A
Directions: You are part of a fireworks crew assembling a local fireworks display.
There are two parts to the fireworks platforms: one part is on the ground and the
other part is on top of a building. You are going to graph all of your results on one
coordinate plane. Make sure to label each graph with its equation. Use the following
equations to assist with this assignment.
• The function for objects dropped from a height where t is the time in
seconds, h is the height in feet at time it t, and h0 is the initial height is
h(t ) =
-16t 2 + h0 .
•
The function for objects that are launched where t is the time in seconds, h is
the height in feet at time t, h0 is the initial height, and v0 is the initial velocity
in feet per second is h(t ) =
-16t 2 + v0t + h0 .
Select the link below to access centimeter grid paper for your portfolio.
Centimeter Grid Paper
Task 1
First, conduct some research to help you with later portions of this portfolio
assessment.
• Find a local building and estimate its height. How tall do you think the
building is?
• Use the Internet to find some initial velocities for different types of fireworks.
What are some of the initial velocities that you found?
Task 2
Respond to the following items.
1. While setting up a fireworks display, you have a tool at the top of the
building and need to drop it to a coworker below.
a. How long will it take the tool to fall to the ground? (Hint: use the first
equation that you were given above, h(t ) =
-16t 2 + h0 . For the building’s
height, use the height of the building that you estimated in Task 1.)
b. Draw a graph that represents the path of this tool falling to the
ground. Be sure to label your axes with a title and a scale. Your graph
should show the height of the tool, h, after t seconds have passed.
Label this line “Tool”.
© 2015 Connections Education LLC. All rights reserved.
2. State whether the parabola represented by h(t ) =
-16t 2 + 250t opens up or
down. Explain why your answer makes sense in the context of this problem.
3. One of the fireworks is launched from the top of the building with an initial
upward velocity of 150 ft/sec.
a. What is the equation for this situation?
b. When will the firework land if it does not explode?
c. Make a table for this situation so that it shows the height from time
t = 0 until it hits the ground.
d. Calculate the axis of symmetry.
e. Calculate the coordinates of the vertex.
f. Explain why negative values for t and h(t ) do not make sense for this
problem.
g. On the same coordinate plane from #1, draw a graph that represents
the path of this firework. Make sure that your graph is labeled
appropriately. Label this graph “Firework #1”.
4. Choose an initial velocity for a firework based on your research from Task 1
a. Write an equation that represents the path of a firework that is
launched from the ground with the initial velocity that you chose.
b. Suppose this firework is set to explode 3 seconds after it is launched.
At what height will this firework be when it explodes?
c. On the same coordinate plane that you have been using, draw a graph
that represents the path of this firework. Mark your graph to indicate
the point at which the firework will explode. Label this graph “Firework
#2”.
5. You launch a third firework. Decide whether you want to launch it from the
ground or from the roof of the building. Also, choose a height at which this
firework will explode and an initial velocity for this firework.
a. How long after setting off the firework should the delay be set?
b. On the same coordinate plane that you have been using, draw a graph
that represents the path of this firework. Mark your graph to indicate
the point at which the firework will explode. Label this graph “Firework
#3”.
6. What can you conclude about how the height of the building and the initial
velocity of the item launched affect the maximum height and the time it
takes to get there?
Task 3
You will submit the following items.
•
results of your research, including the height of the building that you found
and initial velocities for fireworks
© 2015 Connections Education LLC. All rights reserved.
2
•
•
a graph that shows the paths of the tool that was dropped and the three
fireworks that were launched
responses to the items in Task 2
© 2015 Connections Education LLC. All rights reserved.
3

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