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

21.75
21.75

24
24

21.5
21.5

134.25
134.25

Answer 1

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

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

Now, calculate each term step by step:

1. Calculate \( (7.5)^2 \):
\[
(7.5)^2 = 56.25
\]

2. Calculate \( 10 \times 7.5 \):
\[
10 \times 7.5 = 75
\]

3. Substitute these values back into the function:
\[
h(7.5) = -56.25 + 75 + 3
\]

4. Now, simplify:
\[
h(7.5) = -56.25 + 75 = 18.75
\]
\[
h(7.5) = 18.75 + 3 = 21.75
\]

Thus, the height of the ball after 7.5 seconds is \( h(7.5) = 21.75 \).

The correct response is:
**21.75**