Question
A golfer uses tracking device to determine the data of the ball as it is in the air. She calculates that her ball, when 34 yards away from her, reached a maximum height of 72 yards before descending. The path of the golf ball can be modeled by a quadratic function where x represents the horizontal distance and y represents the height of the ball. In terms of the context, which key feature represents the maximum height of the ball?
Answers
GPT-4o mini
In the context of the golfer's ball trajectory, the maximum height of the ball is represented by the vertex of the quadratic function that models the path of the golf ball.
For a quadratic function in the standard form \( y = ax^2 + bx + c \), the vertex gives the point at which the parabola reaches its maximum (if \( a < 0 \)) or minimum (if \( a > 0 \)). In this case, since the ball reaches a maximum height, the vertex corresponds to the coordinates of that maximum point.
Thus, the key feature that represents the maximum height of the ball is the vertex of the quadratic function, which, according to the information given, occurs at a height of 72 yards.
For a quadratic function in the standard form \( y = ax^2 + bx + c \), the vertex gives the point at which the parabola reaches its maximum (if \( a < 0 \)) or minimum (if \( a > 0 \)). In this case, since the ball reaches a maximum height, the vertex corresponds to the coordinates of that maximum point.
Thus, the key feature that represents the maximum height of the ball is the vertex of the quadratic function, which, according to the information given, occurs at a height of 72 yards.