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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?

A bottle rocket is launched straight up. Its height in feet (y) above theground x-example-1

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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.

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