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How to Let Go - AdVision eCommerce

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 5**Question:** A meteorologist is modeling the temperature changes over a day and defines a function \( T(t) = 3t^2 - 12t + 20 \), where \( T \) is the temperature in degrees Celsius and \( t \) is the time in hours from midnight. Determine the time \( t \) when the temperature reaches its minimum.

📌 To find the time \( t \) when the temperature reaches its minimum, we need to find the vertex of the quadratic function \( T(t) = 3t^2 - 12t + 20 \). The vertex form of a quadratic function \( at^2 + bt + c \) gives the time of minimum (or maximum) as \( t = -\frac{b}{2a} \).

📌 Here, \( a = 3 \) and \( b = -12 \). Thus,

📌 t = -\frac{-12}{2 \times 3} = \frac{12}{6} = 2

📌 The minimum temperature occurs at \( t = 2 \) hours from midnight, which is 2 AM. To confirm, we can substitute \( t = 2 \) back into the temperature function:

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