Question

A ball is thrown off a low cliff to the beach below. It is thrown into the air with an

initial upward velocity of 5 meters per second. The following graph models its height
above sea level in meters over time in seconds.
A. Would a linear function, a quadratic function, or an exponential function be
most appropriate as a model for this graph? Explain your choice.
B. Use the graph to create a table containing at least three points that you can
determine exactly from the graph. Include this table as an attachment in your
submission.
C. Use your table to create an equation that models this graph and scenario.
D. Interpret the meaning of the y-intercept of this graph in terms of the given
context.
E. Write your own question that asks a student to interpret a different key feature
of this graph in terms of the given context. Then, provide the solution for your
question.

Answer 1

[AI-generated answer — Bot GPT 3.5]

A. A quadratic function would be most appropriate as a model for this graph because the height of the ball is changing based on gravity acting on it, which is a quadratic relationship with time.

B.
Time (s) Height (m)
0 10
1 8
2 6

C. The equation for this scenario can be written as: h(t) = -5t^2 + 5t + 10, where h(t) represents the height in meters and t represents time in seconds.

D. The y-intercept of this graph is 10, which represents the initial height of the ball above sea level when it was thrown. In other words, this is the height of the cliff from which the ball was thrown.

E. What is the maximum height reached by the ball in this scenario, and what does it represent in terms of the given context?

Solution: The maximum height reached by the ball can be found by finding the vertex of the quadratic function, which in this case occurs when t = 0. Substituting t = 0 into the equation h(t) = -5t^2 + 5t + 10, we get h(0) = 10. Therefore, the maximum height reached by the ball is 10 meters above sea level, which represents the initial height of the ball above sea level before it starts falling back down to the beach.