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what time does the super bowl game start - Coaching Toolbox

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 解: 関数 \(f(x) = 4x^2 + 12x + 9\) の最小値を見つけるために、まず平方完成を行います。この関数は上に開く二次式です（\(x^2\) の係数が正であるため）。

📌 f(x) = 4x^2 + 12x + 9 = 4(x^2 + 3x) + 9

📌 \(x\) の係数の半分を 2 乗したものを加算および減算します:

📌 x^2 + 3x = \left(x + \frac{3}{2}\right)^2 - \frac{9}{4}

📌 f(x) = 4\left(\left(x + \frac{3}{2}\right)^2 - \frac{9}{4}\right) + 9 = 4\left(x + \frac{3}{2}\right)^2 - 9 + 9 = 4\left(x + \frac{3}{2}\right)^2

📌 項 \(4\left(x + \frac{3}{2}\right)^2\) は常に非負であり、\(\left(x + \frac{3}{2}\right)^2 = 0\) のときに最小値 0 を取ります。これは \(x = -\frac{3}{2}\) のときに起こります。

📌 \(x = -\frac{3}{2}\) を元の関数に代入します:

📌 f\left(-\frac{3}{2}\right) = 4\left(-\frac{3}{2} + \frac{3}{2}\right)^2 = 4 \cdot 0 = 0

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