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The graph shows the height \( h \) of a ball thrown into the air, in feet, over time \( t \) in seconds. From the graph, we can observe the ball's height increasing, reaching a maximum height at \( t = 1.5 \) seconds, and then decreasing until it hits the ground at \( t = 3 \) seconds.

To answer the question about the interval where the ball’s height is increasing:

- The ball’s height increases from \( t = 0 \) seconds until it reaches its maximum height at \( t = 1.5 \) seconds.
- The ball's height decreases after \( t = 1.5 \) seconds.

Thus, the ball’s height is increasing on the interval **\( (0, 1.5) \)** seconds.

Let me know if you have any questions or need further clarification!

### Related questions:
1. How can we determine when the ball reaches its maximum height?
2. How can we express the height function algebraically from this graph?
3. How does the vertex of a parabola relate to the maximum or minimum value of a function?
4. What would the interval be if the ball was thrown with more or less force (changing the graph)?
5. Can we calculate the initial velocity of the ball using this graph?

### Tip: 
The point where the ball reaches its maximum height is called the vertex of the parabola, and it can also be found using calculus (by finding the derivative) if the height equation is known.

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

Find the interval where the height of a ball, thrown by Jayden, is increasing by interpreting the quadratic function graph. The height reaches its maximum at t = 1.5 seconds, and the interval of increase is from t = 0 to t = 1.5 seconds. Learn how to analyze quadratic functions and parabolas.

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