https://file.aiquickdraw.com/mathbot/file/1725909319892t1hn7g0u.jpg

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?

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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.

Find the maximum height given the function f(t) = -16(t - 3)^2 + 148.

Explore how to find the maximum height using the quadratic function f(t) = -16(t - 3)^2 + 148. This problem explains the vertex form of a quadratic function and shows that the maximum height is 148 feet when t = 3 seconds. Suitable for Grades 9-11 students learning algebra.

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