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\(A \approx 1104.49\). - Portal da AcÃºstica

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 C(x) = 3x^2 - 12x + k

📌 Substitute \( x = 2 \) into the cost function:

📌 C(2) = 3(2)^2 - 12(2) + k = 3 \cdot 4 - 24 + k = 12 - 24 + k = -12 + k

📌 Set the minimum cost equal to zero:

📌 Thus, the value of \( k \) that ensures the minimum cost is zero is \(\boxed{12}\).

📌 An AI programmer is optimizing a model's performance using a quadratic cost function \( f(x) = ax^2 + bx + c \). If the vertex of this parabola corresponds to the minimum point at \( x = 3 \) and the cost at the vertex is \(-5\), find the relationship between \( a \) and \( c \) given \( b = -6 \).

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