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. Find h(3)

Answer 1

To find the height of the firework at \( t = 3 \) seconds, we can plug \( t = 3 \) into the function \( h(t) \):

\[ h(t) = -16t^2 + 96t \]

Now substituting \( t = 3 \):

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

Calculating \( 3^2 \):

\[ 3^2 = 9 \]

Now substituting that back into the equation:

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

Then, performing the final calculation:

\[ h(3) = 144 \]

Thus, the height of the firework at \( t = 3 \) seconds is \( \boxed{144} \) feet.