Monique is punting a football and the height the ball travels is a function of time. The function h(s)=−s2+10s+3

Question

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

21.5
21.5

21.75
21.75

24
24

134.25

Answer 1

To find the height of the ball after 7.5 seconds, we need to evaluate the function \( h(s) = -s^2 + 10s + 3 \) at \( s = 7.5 \).

Substituting \( s = 7.5 \) into the equation:

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

Calculating each term:

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

Now substituting these values back into the equation:

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

Calculating the result:

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

Therefore, the height of the ball after 7.5 seconds is \( \boxed{21.75} \).