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

21.5
21.5

21.75
21.75

134.25

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 \( h(7.5) \):

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

First, calculate \( (7.5)^2 \): \[ (7.5)^2 = 56.25 \]

Now substitute this value back into the equation: \[ h(7.5) = -56.25 + 10 \cdot 7.5 + 3 \]

Calculate \( 10 \cdot 7.5 \): \[ 10 \cdot 7.5 = 75 \]

Now substitute this value back into the equation: \[ h(7.5) = -56.25 + 75 + 3 \]

Now perform the addition: \[ h(7.5) = -56.25 + 75 = 18.75 \] \[ h(7.5) = 18.75 + 3 = 21.75 \]

So, the height of the ball after 7.5 seconds, \( h(7.5) \), is:

\[ \boxed{21.75} \]