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Home » So 2x² = 348,480 → x² = 174,240 → x = √174,240 ≈ 417.47 - go-checkin.com

So 2x² = 348,480 → x² = 174,240 → x = √174,240 ≈ 417.47 - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 The $ y $-intercept is $ \boxed{8} $.

📌 Question: A game theory economist analyzes the payoff function $ P(x) = -x^2 + 4x + m $. What value of $ m $ ensures the maximum payoff is 12?

📌 Solution: The maximum of $ P(x) = -x^2 + 4x + m $ occurs at the vertex. The $ x $-coordinate of the vertex is $ x = \frac{-b}{2a} = \frac{-4}{-2} = 2 $. Substitute $ x = 2 $ into $ P(x) $:

📌 = -(2)^2 + 4(2) + m

📌 = -4 + 8 + m

📌 The value of $ m $ is $ \boxed{8} $.

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