Applications of quadratics. Baseball player

Question

A baseball player swings and hits a pop fly straight up in the air to the catcher. The height of the baseball in meters t seconds after it is hit is given by the quadratic function h(t) = -4.9t² + 14.7t +1  How long  does it take for the baseball to reach its maximum height?  What is the maximum height obtained by the baseball? 

It takes ___ seconds for the baseball to reach its maximum height

( round to one decimal place as needed)

 

Answer 1

h(t) = -4.9t² + 14.7t + 1      To answer both of your questions, you need to find the vertex of the parabola.

x = -b /2a

t = -14.7/(-9.8)

t = 1.5

 

h(t) = -4.9(1.5)² + 14.7(1.5) + 1

h(t) = -11.025 + 22.05  + 1

h(t) = 12.025

 

(1.5,12.025)    In 1.5 seconds, the baseball will reach its maximum height of 12.025 meters, or 12.0 meters