Question

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

21.5
21.5

24
24

134.25
134.25

21.75

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 \( s = 7.5 \).

Plugging in \( s = 7.5 \):

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

Calculating each term:

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

Now substitute these values back into the equation:

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

Adding these values together:

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

Next, add 3:

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

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