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=((-b)/(2a),(-\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=(-(116^2-4(-16)(7)))/(4(-16))\Rightarrow(-(13904))/(-64)=\text{ 217.25}`

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