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A catapult is sitting on the edge of a cliff and launches a rock over a canyon. The height of the rock from the ground, h(t), over time, t, can be modeled by a quadratic function.

Each of the following functions is a different form of the quadratic model for the situation given above. Which form would be the most helpful if attempting to determine the maximum height of the rock?

1. h(t) = -16(t - 4)2 + 576

2. h(t) = -16t2 + 128t + 320

3. h(t) = -16(t - 10)(t + 2)

4. h(t) = -16t(t - 10) - 32(t -10)

Respuesta :

[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ h(t)=-16\underset{\stackrel{\qquad \uparrow }{\textit{seconds}}}{(t~~ - ~~\stackrel{h}{4})^2}~~ + ~~\underset{\stackrel{\uparrow }{feets~up}}{\stackrel{k}{576}}[/tex]

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