Question

The path of a baseball after it has been hit is modeled by the function h = – 0.0032d2 + 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. What is the maximum height reached by the baseball? How far is the baseball from home plate when it reaches its maximum height?

Answer 1

Answer:

the maximum height of the ball is 81.125 feet above the ground. when the ball is at its peak, the ball is 156.25 feet away from home plate.

Step-by-step explanation:

x = d

y = h

to find the x coordinate of the vertex of a parabola, use the equation

x = -b/2a

y = ax^2 + bx+ c

y = – 0.0032x^2 + x + 3

x = -1 / 2 • - 0.0032

x = 156.25

plug x into original equation to find the the y coordinate of the vertex

y = – 0.0032 • (156.25)^2 + (156.25) + 3

y = – 0.0032 • 24414.0625 + 159.25

y = – 78.125 + 159.25

y = 81.125