Question

Monique is punting a football and the height the ball travels is a function of time. The function h(s)=−s^2+10s+3
gives the height of the ball, h(s)
, given the number of seconds, 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)
.(1 point)
Responses

24
24

21.5
21.5

21.75
21.75

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 need to substitute \( s = 7.5 \) into the function:

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

Calculating \( (7.5)^2 \):

\[
(7.5)^2 = 56.25
\]

Now substituting back:

\[
h(7.5) = -56.25 + 10 \times 7.5 + 3
\]

Calculating \( 10 \times 7.5 \):

\[
10 \times 7.5 = 75
\]

Now substituting that value in:

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

Adding the terms together:

\[
h(7.5) = -56.25 + 75 = 18.75
\]
\[
h(7.5) = 18.75 + 3 = 21.75
\]

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

\[
\boxed{21.75}
\]