Part b) To solve this problem, you have to determine the vertex of the parabola represented by the function
[tex]d(t)=160+48t-16t^2.[/tex]
To determine the vertex, you have to complete the square, and take the above equation to the following form:
[tex]y=l(x-h)^2+k,[/tex]
where (h,k) is the vertex of the parabola.
Completing the square you get:
[tex]\begin{gathered} d(t)=-(16t^2-48t+36)+36+160, \\ d(t)=-(4t-6)^2+196. \end{gathered}[/tex]
Without further calculations, we can conclude that the maximum height will be:
[tex]196ft.[/tex]
at time:
[tex]t=\frac{6}{4}=1.5.[/tex]
Answer:
[tex]\begin{gathered} height=196ft, \\ time=1.5\text{ seconds.} \end{gathered}[/tex]
