Problem

Interpret \(0.25(t-4)^{2}\) in \(h(t)=0.25(t-4)^{2}-6\). State the center and squared distance, express the nonnegative contribution above \(-6\), and infer graph direction and relative width from the fractional scale.

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Center 4; squared distance (t − 4)²; a = 0.25; contribution +0.25(t − 4)²; h(t) + 6 ≥ 0; opens up and is narrower than y = t².

Center 4; squared distance −(t − 4)²; a = −0.25; contribution −0.25(t − 4)²; h(t) + 6 ≤ 0; opens down and is wider than y = t².

Center 4; squared distance (t − 4)²; a = 0.25; contribution +0.25(t − 4)²; h(t) + 6 = 0.25(t − 4)² ≥ 0; opens up and is wider than y = t².

Center 1; squared distance (t − 1)²; a = 0.25; contribution +0.25(t − 1)²; h(t) + 6 ≥ 0; opens up and is wider than y = t².

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