Question

Monique is punting a football and the height the ball travels is a function of time. The function h(s)=−s2+10s+3
ℎ
(
𝑠
)
=
−
𝑠
2
+
10
𝑠
+
3
gives the height of the ball, h(s)
ℎ
(
𝑠
)
, given the number of seconds, s
𝑠
, that the ball has been in the air. After flying through the air for 7.5 seconds, what is the height of the ball? Find h(7.5)
ℎ
(
7.5
)
.(1 point)
Responses

134.25
134.25

21.75
21.75

21.5
21.5

24

Answer 1

To find the height of the ball after 7.5 seconds using the function \( h(s) = -s^2 + 10s + 3 \), we will substitute \( s = 7.5 \) into the function:

\[
h(7.5) = -(7.5)^2 + 10(7.5) + 3
\]

Calculating each term:

1. \( (7.5)^2 = 56.25 \)
2. \( 10(7.5) = 75 \)

Now, substitute those values into the equation:

\[
h(7.5) = -56.25 + 75 + 3
\]

Now, combine the terms:

\[
h(7.5) = -56.25 + 75 + 3 = 21.75
\]

Therefore, the height of the ball after 7.5 seconds is:

\[
\boxed{21.75}
\]