1) Looking at the function y= -16x² + 116x + 7
The maximum height is the vertex described by the parabola. The Vertex follows that formula:
[tex]\begin{gathered} V=(\frac{-b}{2a},\frac{-\Delta}{4a}) \\ \end{gathered}[/tex]
2) Since the question wants only the height, let's keep with the y-coordinate of the Vertex. Let's call it Yv
[tex]Y_V=\frac{-(116^2-4(-16)(7))}{4(-16)}\Rightarrow\frac{-(13904)}{-64}=\text{ 217.25}[/tex]
So the maximum height of that rocket is 217.25 feet above the ground.
