Question

The path of a baseball after it has been hit is modeled by the functionh= -0.0032d^{2} d 3h=−0.0032d 2 d 3, where h is the height in feet of the baseball and d is the distance in feet the baseball is from home plate. how far is the baseball from home plate when it reaches its maximum height (x of vertex? 156.25 156.25 feet (round to the nearest hundredth) what is the maximum height reached by the baseball (y of vertex)? 81.125 81.125 feet (round to the nearest hundredth)

Answer 1

The baseball is 0 feet from home plate when it reaches its maximum height of 0 feet.

Step-by-step explanation:

The maximum height of the baseball can be found by determining the vertex of the quadratic function h = -0.0032d^2. Since the vertex is given by the formula x = -b/2a, where a = -0.0032 and b = 0, we can substitute these values into the formula to find the x-coordinate of the vertex, which represents the distance from home plate when the baseball reaches its maximum height.

x = -0/2(-0.0032) = 0

Therefore, the baseball is 0 feet from home plate when it reaches its maximum height.

To find the maximum height, we substitute the x-coordinate of the vertex into the given equation:

h = -0.0032(0)^2 = 0

Therefore, the maximum height reached by the baseball is 0 feet.