Question

Monique is punting a football and the height the ball travels is a function of time. The
function gives the height of the ball, , given the number of
seconds, , 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 . (1 point)
h (s) = −s + 10s + 3
2 h (s)
s
h (7.5)
24
21.75
21.5
134.25

Answer 1

To find the height of the ball at \( s = 7.5 \) seconds using the function \( h(s) = -s^2 + 10s + 3 \), we can plug in 7.5 for \( s \):

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

Calculating \( (7.5)^2 \):

\[
(7.5)^2 = 56.25
\]

Now plug that into the equation:

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

Calculating \( 10(7.5) \):

\[
10(7.5) = 75
\]

Now, substitute back:

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

Combine the values:

\[
h(7.5) = -56.25 + 75 + 3 = -56.25 + 78 = 21.75
\]

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

\[
h(7.5) = 21.75
\]

The correct answer is **21.75**.