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📅 April 30, 2026 👤 scraface

Apr 30, 2026

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📌 The given function is \(f(x) = 2x^2 - 12x + 18\), which is a quadratic function in standard form \(ax^2 + bx + c\), with \(a = 2\), \(b = -12\), and \(c = 18\).

📌 The vertex of a parabola \(y = ax^2 + bx + c\) occurs at:

📌 x = -\frac{b}{2a} = -\frac{-12}{2 \cdot 2} = \frac{12}{4} = 3

📌 Now substitute \(x = 3\) into the function to find the corresponding \(y\)-coordinate:

📌 f(3) = 2(3)^2 - 12(3) + 18 = 2(9) - 36 + 18 = 18 - 36 + 18 = 0

📌 Thus, the vertex is at \((3, 0)\), indicating that the optimal credit score is 3 (in appropriate scale), where the modeled repayment cost is minimized at 0 cost, likely representing break-even.

📌 The vertex is \(\boxed{(3,\ 0)}\).

📌 A statistician develops a new robust estimator and models its bias under repeated samples by evaluating the sum \(\sum_{k=1}^{50} \frac{1}{k(k+2)}\). Compute this sum exactly.

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