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Home » Evolving Pupitar: The Game-Changing Tool Every Teacher Needs Now! - Sterling Industries

Evolving Pupitar: The Game-Changing Tool Every Teacher Needs Now! - Sterling Industries

📅 April 16, 2026 👤 scraface

Apr 16, 2026

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📌 A programmer is optimizing a neural network and models the loss function as \( L(x) = 2x^2 - 8x + k \). Find \( k \) if the minimum loss occurs at \( x = 2 \) and the loss there is 4.

📌 The vertex form of a quadratic function \( ax^2 + bx + c \) occurs at \( x = -\frac{b}{2a} \). For \( L(x) = 2x^2 - 8x + k \),

📌 \[ a = 2, \, b = -8 \]

📌 \[ x_{vertex} = -\frac{-8}{2 \times 2} = 2 \]

📌 The minimum loss occurs at \( x = 2 \), and \( L(2) = 4 \). Substitute \( x = 2 \) into \( L(x) \):

📌 \[ L(2) = 2(2)^2 - 8(2) + k = 4 \]

📌 \[ 2 \times 4 - 16 + k = 4 \]

📌 \[ 8 - 16 + k = 4 \]

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