Question

2 jorden advance’s hit reached a maximum height of 86 feet, and this maximum occurred when the ball was 178 feet from home plate. determine the coordinates of the vertex (h, k). explain how you know

Explanation:

Step1: Identify the problem type

This is a problem about finding the vertex of a parabola (since it's about the height of a hill, likely a quadratic function representing a parabola). The vertex form of a parabola is \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex.

Step2: Analyze the given information

The maximum height (which is the \( y \)-coordinate of the vertex, \( k \)) is 86 feet. The maximum occurs when the hill is 175 feet from the home plate (this is the \( x \)-coordinate of the vertex, \( h \)).

Step3: Determine the vertex coordinates

For a parabola representing the height of the hill as a function of distance from home plate, the vertex \((h, k)\) will have \( h = 175 \) (distance from home plate at maximum height) and \( k = 86 \) (maximum height). So the vertex coordinates are \((175, 86)\). We know this because the vertex of a parabola (quadratic function) represents the maximum (if the parabola opens downward) or minimum (if it opens upward) point. Since the hill reaches a maximum height, the parabola opens downward, and the vertex is the maximum point, so the \( x \)-value is the distance from home plate at maximum height, and the \( y \)-value is the maximum height.

Answer:

The coordinates of the vertex \((h, k)\) are \((175, 86)\) because the vertex of the parabola (representing the hill's height as a function of distance from home plate) has \( h \) as the distance from home plate at maximum height (175 feet) and \( k \) as the maximum height (86 feet).