Question

A bottle rocket is launched straight up. Its height in feet (y) above theground x seconds after launch is modeled by the quadratic function: y =-16x2 + 116x + 7.What was the maximum height of the rocket?

Answer 1

1) Looking at the function y= -16x² + 116x + 7

The maximum height is the vertex described by the parabola. The Vertex follows that formula:

$\begin{gathered} V=(\frac{-b}{2a},\frac{-\Delta}{4a}) \\ \end{gathered}$

2) Since the question wants only the height, let's keep with the y-coordinate of the Vertex. Let's call it Yv

$Y_V=\frac{-(116^2-4(-16)(7))}{4(-16)}\Rightarrow\frac{-(13904)}{-64}=\text{ 217.25}$

So the maximum height of that rocket is 217.25 feet above the ground.