Elena is the champion diver on her swim team. she dives from a diving board that is 48 feet high. her position in the pool is represented by the function h(t)=-16t^2+24t+40, where t represents time in seconds and h(t) represents height in feet.
part a: after how many seconds does elena enter the pool?
part b: what is the greatest height elena reaches her dive?
part c: how long will it take elena to reach the maximum height?

A. enter pool is when h(t)=0
B. max height is the vetex
C. that is the t value of the vertex

A.
0=-16t²+24t+40
using math
t=-1 or 5/2
can't be negative time
t=5/2
after 2.5 seconds

B. find vertex
get into form
y=a(x-h)^2+k
complete the square
h(t)=-16t²+24t+40
h(t)=(-16t²+24t)+40
h(t)=-16(t²-1.5t)+40
h(t)=-16(t²-1.5t+0.5625-0.5625)+40
h(t)=-16((t-0.75)²-0.5625)+40
h(t)=-16(t-0.75)²+9+40
h(t)=-16(t-0.75)²+49

vertex is at t=0.75 and h(0.75)=49

A. after 2.5 seconds
B. 49ft
C. 0.75 seconds