# The height in feet of a golf ball hit into the air is given by #h= -16t^2 + 64t#, where t is the number of seconds elapsed since the ball was hit. What is the maximum height of the ball?

##### 2 Answers

#### Explanation:

maximum or minimum height when

when

when t =2,

#### Explanation:

Find the roots of the parabola by setting h = 0

#rArr-16t^2+64t=0# Factorising gives.

#-16t(t-4)=0#

#rArrt=0" or " t=4# Since the parabola is symmetrical the axis of symmetry will pass through the maximum. The axis of symmetry is positioned at the mid- point of the roots.

#rArrcolor(red)(t=2)#

#rArr"max. height "=-16color(red)((2))^2+64(color(red)(2))#

#color(white)(xxxxxxxxxxxx)=(-16xx4)+(64xx2)#

#color(white)(xxxxxxxxxxxx)=-64+128#

#color(white)(xxxxxxxxxxxx)=64#

#rArr"maximum height of ball " =64" feet"#