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Home » 9(x^2 - 6x) - Baxtercollege

9(x^2 - 6x) - Baxtercollege

📅 March 10, 2026 👤 scraface

Mar 10, 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 \( L(x) \):

📌 \[ L(2) = 2(2)^2 - 8(2) + k = 4 \]

📌 \[ 2 \times 4 - 16 + k = 4 \]

📌 \[ 8 - 16 + k = 4 \]

🔥 Popular Posts

B = 3 \cdot 7 - 3 = 21 - 3 = 18
Now apply Pick’s Theorem:
9\sqrt{3} = I + \frac{18}{2} - 1 = I + 9 - 1 = I + 8
I = 9\sqrt{3} - 8
But $I$ must be an integer, and $9\sqrt{3} \approx 9 \cdot 1.732 = 15....
Instead, interpret the problem as a combinatorial lattice: suppose the...
From combinatorial geometry, the number of lattice points strictly ins...
Number of interior points (in unit triangular lattice): $ \frac{(n-2)(...
Alternatively, for a large equilateral triangle of side $n$ in a trian...
I = \frac{(n-1)(n-2)}{2}

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