Problem

Interpret \((n-10)^{2}\) in \(h(n)=0.5(n-10)^{2}-1\) using the displayed graph. Name the center, distinguish signed displacement from distance, and show why \(10\text{-}d\) and \(10+d\) produce equal outputs.

Unannotated graph of h(n)=0.5(n−10)²−1; the parabola is shown without naming its center, symmetry axis, or equal-output inputs.

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Center 10; signed difference n − 10; distance n − 10 without absolute value; squared term (n − 10)²; inputs 10 − d and 10 + d are claimed to have different outputs.

Center 10; signed difference n − 10; distance |n − 10|; squared-distance term (n − 10)²; inputs 10 − d and 10 + d have equal outputs.

Center 10; signed difference n − 10; distance |n − 10|; squared term is interpreted as the linear distance n − 10; inputs 10 − d and 10 + d are claimed to have different outputs.

Center −10; signed difference n + 10; distance |n + 10|; squared term (n + 10)²; inputs −10 − d and −10 + d have equal outputs.

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Interpret \((n-10)^{2}\) in \(h(n)=0.5(n-10)^{2}-1\) using the displayed graph. Name the center, distinguish signed displacement from distance, and show why \(10\text{-}d\) and \(10+d\) produce equal outputs.

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