The function provided in the image is:

$f(t) = -16(t - 3)^2 + 148$

This appears to be a quadratic function in vertex form. The general form of a quadratic function is:

$f(t) = a(t - h)^2 + k$

Where $(h, k)$ is the vertex of the parabola. In this case, $a = -16$, $h = 3$, and $k = 148$. Since the coefficient of $(t - h)^2$ is negative, this parabola opens downward, meaning that the vertex $(3, 148)$ is the maximum point.

To clarify what is being asked:

The number to be typed in the box is likely related to the maximum height (in feet) of the function. The vertex $(3, 148)$ tells us that the maximum height is 148 feet when $t = 3$ seconds.

Would you like further clarification on how this quadratic function behaves or any other details?

Here are some related questions you might consider:

1. What is the significance of the vertex in a quadratic function?
2. How do you find the axis of symmetry in a quadratic equation?
3. What does the coefficient $-16$ represent in this equation?
4. Can this quadratic function model a real-world scenario? If so, what?
5. How would you solve for the time when the function hits the ground (i.e., $f(t) = 0$)?

Tip: The vertex form of a quadratic function is useful for quickly identifying the maximum or minimum value without needing to complete the square.