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

Question

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

134.25
134.25

21.5
21.5

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 \( s = 7.5 \).

Let's calculate \( h(7.5) \):

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

Calculating \( (7.5)^2 \):

\[ (7.5)^2 = 56.25 \]

Now substituting this back into the function:

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

Calculating \( 10(7.5) \):

\[ 10(7.5) = 75 \]

Now substituting that into the function:

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

Calculating \( -56.25 + 75 \):

\[ -56.25 + 75 = 18.75 \]

Now adding 3:

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

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

Thus, the answer is:

21.75