Solution
Given
![h(t)=-16t^2+128\sqrt[]{3}t](https://img.qammunity.org/2023/formulas/mathematics/college/1s84nnl2vre4dx2fdbcrrtdf7ki6vujefs.png)
Analyse
The function is quadratic and to get the maximum height as well as the time taken to get the maximum height, we will have to write h(t) in this form

Solve
![\begin{gathered} h(t)=-16t^2+128\sqrt[]{3}t \\ h(t)=-16(t^2-8\sqrt[]{3}t) \\ h(t)=-16\lbrack t^2-8\sqrt[]{3}t+(4\sqrt[]{3})^2-(4\sqrt[]{3})^2\rbrack \\ h(t)=-16\lbrack t^2-8\sqrt[]{3}t+(4\sqrt[]{3})^2\rbrack+16(4\sqrt[]{3})^2 \\ h(t)=-16(t-4\sqrt[]{3})^2+768 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/a63c61eaxjqh2n77nnnb2j4ocsbeym3alb.png)
![\begin{gathered} time=4\sqrt[]{3}=6.9282\text{ secs} \\ time=7\text{ secs (to the nearest second)} \\ MaxHeight=\text{ 768 fe}ets \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/bqwivny9t1bxa2axtteky1oz83tv6xiuna.png)
Paraphrase
Therefore, It would take the fireworks 7 seconds to get to it's maximum height and the Maximum Height of the is 768 feets