Naming, Evaluating, & Interpreting Functions Quick Check

Question

5 of 55 of 5 Items

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

134.25
134.25

21.75
21.75

21.5
21.5

24
24

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 \( s = 7.5 \).

Start by substituting \( s = 7.5 \) into the function:

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

Now calculate each term:

1. \( (7.5)^2 = 56.25 \)
2. \( 10 \times 7.5 = 75 \)

Now substitute these values into the equation:

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

Now calculate it step by step:

1. \( -56.25 + 75 = 18.75 \)
2. \( 18.75 + 3 = 21.75 \)

Thus, the height of the ball after 7.5 seconds is

\[ \boxed{21.75} \]