h=-16t^2+32t

Question

Find maximum height and the time is reaches the maximum height

 

Answer 1

In f(x) = ax² + bx + c, the maximum occurs at x = -b/2a.

In this problem x = -32/2(-16), or x = 1

f(1 = ?

Answer 2

The time to the maximum height is exactly one half of the time it takes to come back to the ground.

 

When it reaches the ground again h=0

 

-16t^2+32t=0

 

16t(2-t)=0

 

t= 0 or 2 s

 

t=0 is the start time so t=2 is the time we want.

 

Time to maximum height = 1 time unit (seconds I guess)

 

The maximum height is found by substituting t=1 in the equation

 

h=-16(1^2)+32(1)=16