https://file.aiquickdraw.com/mathbot/file/17286655387630q6ey7zp.jpg

The function provided is:

\[
h(t) = -16t^2 + 100
\]

where \( h(t) \) gives the height of the tool in feet at time \( t \) seconds after it was dropped.

To find the height of the tool at \( t = 2 \) seconds, substitute \( t = 2 \) into the function:

\[
h(2) = -16(2)^2 + 100
\]

\[
h(2) = -16(4) + 100 = -64 + 100 = 36
\]

Thus, the height of the tool after 2 seconds is **36 feet**.

Would you like further details or explanations on this? 

Here are 5 related questions you could explore:

1. What is the height of the tool at \( t = 0 \)?
2. How long will it take for the tool to hit the ground (i.e., when \( h(t) = 0 \))?
3. What is the maximum height reached by the tool if it had been thrown upwards initially?
4. How would the height change if the platform were higher (changing the constant)?
5. How would the height change if air resistance were included in the model?

**Tip:** Quadratic functions like this often model free fall, where the negative coefficient represents the effect of gravity pulling the object down.

The polynomial function h(t) = -16t^2 + 100 gives the height of a tool t seconds after it was dropped. What is the height at t = 2?

Find the height of a tool after 2 seconds when dropped from a platform using the quadratic function h(t) = -16t^2 + 100. This solution explains free fall motion, algebraic substitution, and how to interpret quadratic functions. Suitable for Grades 9-10.

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