Questions: A tennis ball is tossed upward, and its heights at various times are recorded. Let f(t) be the height (in feet) of the tennis ball at t seconds. Complete parts a through e. Time (seconds) Height (feet) 0.00 1.93 0.06 2.36 0.12 2.49 0.18 2.64 0.24 2.65 0.30 2.60 0.36 2.46 a. Find an equation of f. Choose the correct answer below. A. f(t)=-13.33 t^2+8.13 t-8.03 B. f(t)=-13.33 t^2+6.13 t+1.97 C. f(t)=13.33 t+8.13 D. f(t)=6.13(-8.03)^t

Find an equation of \( f \).

Identify the type of function.

The data represents the height of a tennis ball over time, which typically follows a quadratic function due to the effects of gravity. Therefore, we expect \( f(t) \) to be a quadratic function of the form \( f(t) = at^2 + bt + c \).

Analyze the given options.

The options provided are:

A. \( f(t) = -13.33 t^{2} + 8.13 t - 8.03 \)

B. \( f(t) = -13.33 t^{2} + 6.13 t + 1.97 \)

C. \( f(t) = 13.33 t + 8.13 \)

D. \( f(t) = 6.13(-8.03)^{t} \)

Options A and B are quadratic functions, while C is linear, and D is an exponential function. Since the height of a tossed ball follows a quadratic path, options C and D can be eliminated.

Determine the correct quadratic function.

To determine the correct quadratic function, we can check the initial condition. At \( t = 0 \), the height is 1.93 feet. Substituting \( t = 0 \) into the quadratic functions:

For A: \( f(0) = -8.03 \) (does not match 1.93)

For B: \( f(0) = 1.97 \) (approximately matches 1.93)

Thus, option B is the most suitable choice.

\(\boxed{f(t) = -13.33 t^{2} + 6.13 t + 1.97}\)

The equation of \( f \) is \(\boxed{f(t) = -13.33 t^{2} + 6.13 t + 1.97}\).