Problem

\(D(x)=2(x-4)^{2}+15\) models predicted defect count \(D\) for machine settings \(0\le~x\le~10\). Verify the vertex lies in the contextual domain, then identify vertex, opening, extremum type, contextual input/unit, contextual output/unit, and model interpretation.

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vertex=(-4,15); opening=up; extremum type=minimum on domain; contextual input=machine setting-4; contextual output=predicted15 defects; interpretation=model predicts minimum15 defects at setting-4

vertex=(4,15); opening=up; extremum type=minimum on domain; contextual input=machine setting4; contextual output=15 defects; interpretation=machine is guaranteed to produce exactly15 defects at setting4

vertex=(4,15); opening=up; extremum type=maximum on domain; contextual input=machine setting4; contextual output=predicted15 defects; interpretation=model predicts maximum15 defects at setting4

vertex=(4,15); opening=up; extremum type=minimum on domain; contextual input=machine setting4; contextual output=predicted15 defects; interpretation=model predicts minimum15 defects at setting4

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\(D(x)=2(x-4)^{2}+15\) models predicted defect count \(D\) for machine settings \(0\le~x\le~10\). Verify the vertex lies in the contextual domain, then identify vertex, opening, extremum type, contextual input/unit, contextual output/unit, and model interpretation.

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