https://file.aiquickdraw.com/mathbot/file/1733329757394qp2wmblb.jpg

From the graph provided in the question:

1. **Symmetry of the graph**:
   - The parabola representing the height of the javelin is symmetric about its vertex. From the graph, the vertex occurs at \( t = 2 \) seconds.
   - Therefore, the height of the javelin is symmetric about the line \( t = 2 \) seconds.

2. **When the javelin is 20 feet above the ground**:
   - Observing the graph, the javelin reaches a height of 20 feet for the first time as it rises, and then again as it falls.
   - From the graph, these points occur approximately at \( t = 1 \) second (first time) and \( t = 3 \) seconds (second time).

### Final Answers:
1. The height of the javelin above the ground is symmetric about the line \( t = 2 \) seconds.
2. The javelin is 20 feet above the ground for the first time at \( t = 1 \) second and again at \( t = 3 \) seconds.

Would you like a detailed explanation or have any additional questions?

### Related Questions:
1. What is the maximum height reached by the javelin, and at what time does it occur?
2. How long does the javelin stay in the air before hitting the ground?
3. How would you determine the height of the javelin at a specific time (e.g., \( t = 1.5 \))?
4. Can you derive the quadratic equation that models the javelin's motion using its vertex and a point?
5. How does the initial velocity affect the shape of the graph?

**Tip:** To analyze a quadratic graph, always identify the vertex, axis of symmetry, and points of intersection with key heights or the ground.

A track-and-field athlete releases a javelin. The height of the javelin as a function of time is shown on the graph. Use the graph to complete the following statements:
1. The height of the javelin above the ground is symmetric about the line t = __ seconds.
2. The javelin is 20 feet above the ground for the first time at t = __ seconds and again at t = __ seconds.

Explore how to interpret a quadratic graph modeling the height of a javelin. Learn to identify symmetry, find when the javelin reaches specific heights, and analyze the parabolic motion. Ideal for students in Grades 9-11 studying quadratic functions.

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