Problem

A modeled vertical displacement is \(D(x)=2(x+1)^{2}-18~\text{meters}\) along coordinates \(-5\le~x\le~3\). Find and interpret its zeros.

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zero equation=2(x+1)²=18 so (x+1)²=18; candidates=x=-1±3sqrt(2); domain check=neither candidate is in[-5,3]; zeros=none; interpretation=displacement never reaches zero in the modeled interval

zero equation=2(x+1)²=18 so (x+1)²=9; candidates=x=-1±3=-4,2; domain check=both in[-5,3]; zeros=(-4,0),(2,0); interpretation=displacement is zero at coordinates-4 and2

zero equation=(x+1)²=0; candidate=x=-1; domain check=-1 is in[-5,3]; zero=(-1,0); interpretation=displacement is zero at coordinate-1

zero equation=(x+1)²=9; candidates=x=-1±9=-10,8; domain check=neither candidate is in[-5,3]; zeros=none; interpretation=displacement never reaches zero in the modeled interval

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A modeled vertical displacement is \(D(x)=2(x+1)^{2}-18~\text{meters}\) along coordinates \(-5\le~x\le~3\). Find and interpret its zeros.

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