Question

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?

Answer 1

Step-by-step explanation: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

Answer 2

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