SOLUTION: 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

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: 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       Log On


   

Question 1199226: 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 by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
We can model the path of the baseball as a parabola. The maximum height is the y-coordinate of the vertex of the parabola, and the distance of the baseball from home plate when it is at its maximum height is the x-coordinate.
For a quadratic ax%5E2%2Bbx%2Bc, the vertex is at -b%2F2a. In this case, b=1 and a=-0.0032. Plugging this into a calculator, we see that -b%2F2a is 156.25, which is the x-coordinate of the vertex. To get the y-coordinate, we simply put in x=156.25 into the quadratic, to get y=81.125. Therefore, the maximum height of the baseball is highlight%2881.125%29 feet, and it is highlight%28156.25%29 feet from the home plate when it happens.