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

21.5
21.5

134.25
134.25

21.75
21.75

24

Answer 1

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

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

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

Calculating each part step by step:

1. Calculate \( (7.5)^2 \): \[ (7.5)^2 = 56.25 \]

2. Calculate \( 10(7.5) \): \[ 10(7.5) = 75 \]

3. Now substitute back into the height function: \[ h(7.5) = -56.25 + 75 + 3 \]

4. Combine the terms: \[ h(7.5) = -56.25 + 75 + 3 = 18.75 + 3 = 21.75 \]

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

The correct response is: \[ \boxed{21.75} \]