Final answer:
In one-on-one basketball, using the provided data, we can infer that the ball's height is increasing up to a point slightly before the 12 feet mark from the shooter and starts to decrease thereafter. The maximum height reached by the ball is at a height of 14 feet.
Step-by-step explanation:
To determine for what horizontal distances the height of the ball is increasing and decreasing when playing basketball and the ball follows a parabolic path, you can use the information given in the question to construct a quadratic model representing the ball's trajectory.
The horizontal distances and corresponding heights are provided. Notice that the ball's height increases up to a certain point and then starts decreasing. To find out where it increases or decreases, we look for the vertex of the parabola. The vertex will provide the maximum height of the ball. Since we have symmetric points around the horizontal distance of 12 feet ((6, 12) and (12, 10)), we can infer that at 12 feet from the shooter, the ball starts descending, meaning the vertex and maximum point occur just before that distance.
The maximum height can be found between the distances of 6 and 12 feet, which is the point (9,14) - the height is 14 feet, considering that it increases before that and starts decreasing after.
Therefore, the ball's height is increasing from the shooter up to a point slightly before 12 feet, and it is decreasing after that point as it approaches the center of the hoop.