At the county July 4th celebration, a firework is launched. The function h(t) = -16t^2 + 96t gives the height in feet of the firework, t seconds after it has been launched. What does h(3) represent in context of this situation?

Answer 1

The function \( h(t) = -16t^2 + 96t \) represents the height of the firework in feet at any time \( t \) seconds after it has been launched.

To understand what \( h(3) \) represents, we can substitute \( t = 3 \) into the function:

\[ h(3) = -16(3^2) + 96(3) \] \[ h(3) = -16(9) + 96(3) \] \[ h(3) = -144 + 288 \] \[ h(3) = 144 \]

So, \( h(3) = 144 \) feet.

In the context of this situation, \( h(3) \) represents the height of the firework 3 seconds after it has been launched. Specifically, it means that at 3 seconds, the firework reaches a height of 144 feet.