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