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Home » Thus, the $ y $-intercept point is $ oxed(0, 1) $. - Midis

Thus, the $ y $-intercept point is $ oxed(0, 1) $. - Midis

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 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.

📌 oxed{rac{3}{8}}

📌 Question:** A deep-sea microbial ecologist models the growth of bacteria near hydrothermal vents with the function \( f(x) = 5x^3 - 15x^2 + 10x \). Determine the critical points of \( f(x) \) to analyze potential growth spurts.

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