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toby keith courtesy of the red white and blue lyrics - American Beagle Club

📅 February 26, 2026 👤 scraface

Feb 26, 2026

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📌 The $ y $-intercept is the point $ (0, b) $, so it is $\boxed{5}$.

📌 Question: A science educator uses a function $ h(x) = x^2 - 4x + c $ to model student performance, and finds that the minimum score occurs at $ x = 2 $. What value of $ c $ ensures $ h(2) = 3 $?

📌 Solution: The vertex of a parabola $ h(x) = x^2 - 4x + c $ occurs at $ x = \frac{-(-4)}{2(1)} = 2 $, which matches the given condition. Now substitute $ x = 2 $ and set $ h(2) = 3 $:

📌 h(2) = (2)^2 - 4(2) + c = 3

📌 - 8 + c = 3

📌 Thus, the value of $ c $ is $\boxed{7}$.Question: A quantum error correction code requires the evaluation of a cubic polynomial $ f(x) $ such that $ f(1) = 3 $, $ f(2) = -1 $, $ f(3) = 5 $, and $ f(4) = -7 $. Determine $ f(5) $.

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