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The graph shows the trajectory of a ball thrown by Genesis, with the ball's height \( h \) in meters on the vertical axis and time \( t \) in seconds on the horizontal axis. The ball reaches its maximum height of approximately 11.025 meters at \( t = 1.5 \) seconds, and falls back to the ground at \( t = 3 \) seconds.

To determine the interval where the ball's height is decreasing, we need to focus on when the ball starts falling back down after reaching its maximum height.

### Answer:
The ball's height is decreasing for \( t \in (1.5, 3] \). This means from just after 1.5 seconds to 3 seconds, the ball is falling back to the ground.

Would you like further details on how this was determined or a more detailed explanation of the graph?

Here are five related questions to deepen understanding:

1. What does it mean for a function to be increasing or decreasing?
2. How do you determine intervals of increase or decrease using a graph?
3. What would the derivative of the height function \( h(t) \) represent in this scenario?
4. How can we calculate the maximum height using the properties of parabolas?
5. Can we determine the velocity of the ball at specific points using this graph?

**Tip:** The point where the ball reaches its maximum height corresponds to the vertex of a parabolic path, and the slope of the tangent line at this point is zero.

Genesis throws a ball up in the air. The graph below shows the height of the ball h in meters after t seconds. Find the interval for which the ball’s height is decreasing.

Find the interval where a ball’s height is decreasing based on the quadratic function representing the height in a graph. This example covers graph interpretation and understanding of parabolas and their key properties. Suitable for students in Grades 9-12.

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