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the things they carried tim o'brien - Coaching Toolbox

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Total needed for average of 88 over 5 tests = 88 Ã 5 = <<88 Ã 5 = 440>>440.

📌 Sum of first four scores = 85 + 90 + 78 + 92 = <<85 + 90 + 78 + 92 = 345>>345.

📌 Score needed on fifth test = 440 â 345 = <<440 â 345 = 95>>95.

📌 #### 95**Question:** An ornithologist is tracking bird migration patterns and models the position of a bird using the function \( h(t) = 4t^2 - 3t + 2 \). Find the time \( t \) when the bird is at its minimum height during the flight from \( t = 0 \) to \( t = 3 \).

📌 Solution:** To find the time \( t \) when the bird is at its minimum height, we need to determine the vertex of the quadratic function \( h(t) = 4t^2 - 3t + 2 \). The vertex form for a quadratic equation \( at^2 + bt + c \) occurs at \( t = -rac{b}{2a} \).

📌 Here, \( a = 4 \) and \( b = -3 \). Thus,

📌 t = -rac{-3}{2 imes 4} = rac{3}{8}

📌 Since \( rac{3}{8} \) is within the interval from \( t = 0 \) to \( t = 3 \), this is the time when the bird reaches its minimum height.

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