For t in seconds the height of a baseball in feet is given b

For t in seconds, the height of a baseball in feet is given by the form h(t) = -16t^2 + 48t + 3 Rewrite the formula above in vertex format. Find and interpret the vertical intercept. Find when the ball hits the ground. When does the ball reach maximum height, and what is this maximum height? Identify scale, and information you found above in the graph provided.

Solution

h(t) = -16t² + 48t + 3 = -16*(t² + 3t + 3/16 ) = -16*( (t+ 3/2)² - 33/16 ) = - 16*(t+1.5)² + 33

now the term -16*(t+1.5)² is always negative so max height will occur when the term -16*(t+1.5)² becomes zero

so h max = 33 and this will happen when t = -1.5 so vertex coordinate will be ( -1.5 , 33)

For vertical intercept t= 0 so h =-16*(0+1.5)² + 33 = -3

when ball hits the ground h =0 so -16*(t+1.5)² + 33 = 0

on solving t = 3.06