Mathematics, 23.06.2019 23:50 leem6
The surface of a pedestrian bridge forms a parabola. let the surface at one side of the bridge be represented by the origin (0,0) and the surface at the other side be represented by (16,0). the center of the bridge is 2 feet higher than each side and can be represented by a vertex of (8,2). write a function in vertex form that models the surface of the bridge. .
Answers: 1
![\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} \stackrel{\textit{we'll use this one}}{y=a(x- h)^2+ k}\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{}{ h},\stackrel{}{ k}) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=8\\ k=2 \end{cases}\implies y=a(x-8)^2+2\qquad (16,0)~~ \begin{cases} x=16\\ y=0 \end{cases}](/tpl/images/0009/7679/4fe7c.png)
![\bf 0=a(16-8)^2+2\implies -2 = a(8)^2\implies -2=64a \\\\\\ \cfrac{-2}{64}=a\implies \cfrac{-1}{32}=a \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill y=-\cfrac{1}{32}(x-8)^2+2~\hfill](/tpl/images/0009/7679/6de43.png)
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The surface of a pedestrian bridge forms a parabola. let the surface at one side of the bridge be re...
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