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

21.75
21.75

24
24

21.5
21.5

134.25
134.25
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page 15 of 15

Answer 1

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

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

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

Calculate \( (7.5)^2 \):

\[ (7.5)^2 = 56.25 \]

Now substitute this back into the equation:

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

Calculate \( 10(7.5) \):

\[ 10(7.5) = 75 \]

Now substitute this value:

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

Combine the terms:

\[ h(7.5) = -56.25 + 75 + 3 = 75 - 56.25 + 3 = 75 - 53.25 = 21.75 \]

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

\[ \boxed{21.75} \]