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The problem shown asks for the horizontal distance (x-axis) that the ball has traveled when it hits the ground after being thrown from an initial height of 6 meters.

The graph represents a quadratic function, which is a typical model for projectile motion, indicating the height of the ball (y-axis) as a function of the horizontal distance traveled (x-axis). The vertex of the parabola is the highest point, and the ball hits the ground when the height \( y = 0 \).

### Step-by-step solution:

1. **Initial height**: The ball starts at \( y = 6 \), as shown in the graph at \( x = 0 \).
2. **Vertex**: The vertex is at \( x = 3 \), which is the maximum height.
3. **Ball hits the ground**: We are interested in the horizontal distance (x-axis value) when \( y = 0 \), which happens around \( x = 6 \) meters.

Thus, the ball travels a horizontal distance of **6 meters** before hitting the ground.

### Answer:
The correct option is **C. 6 meters**.

Would you like more details or have any questions?

Here are 5 related questions for deeper understanding:
1. What is the significance of the vertex in a projectile motion graph?
2. How can you derive the quadratic equation that models the motion from the graph?
3. What role does gravity play in the shape of this trajectory?
4. How would the graph change if the ball were thrown at a higher speed?
5. How do you calculate the maximum height using the vertex?

**Tip**: In projectile motion, the horizontal distance traveled is often called the "range," and it depends on both the initial velocity and the height.

A ball is thrown from an initial height of 6 meters. How far does the ball travel (horizontally) until it hits the ground?

This problem involves determining the horizontal distance traveled by a ball thrown from an initial height of 6 meters, modeled as a quadratic equation. The solution includes using the vertex and zeroes of the parabola to find the horizontal distance before the ball hits the ground. Suitable for students in Grades 9-12.

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