Robyn W. Carlin, Grades 9-10, Mathematics
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Answers: Celebrating the Fourth of July!
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Scenario: Marie is standing on the balcony of her apartment. She shoots a firecracker straight up from a height of 128 feet with an initial velocity of 32 feet per second.

The quadratic equation that represents this scenario is: h = 16t2 + 32t + 128

Write the answers to all questions in complete sentences. Make sure you can support your answers.

1. What is the height of the firecracker after 2.5 seconds? h = 108 feet

2. At what time does the firecracker reach a height of 108 feet? t = 2.5 seconds

3. When does the firecracker reach its maximum height? t = 1 second

4. What is the maximum height of the firecracker? Maximum height = 144 feet

5. At what time does the firecracker hit the ground? t = 4 seconds

6. A bird is flying overhead at an altitude of 150 feet. Is the bird in danger of being hit by the firecracker? Support your answer.
No, the bird is not in danger of being hit by the firecracker. The firecracker reaches a maximum height of 144 feet, 6 feet below the flying altitude of the bird.

7. What are the domain and range for this scenario? Support your answer.
The domain is 0 < t < 4. Time is representative of the domain; the firecracker is in flight between 0 and 4 seconds. The range of this is 0 < t < 144. Height is representative of the range, and the firecracker reaches a minimum height of 0 (when it hits the ground) and a maximum height of 144 feet.