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Укажи, якого найменшого значення набувае вираз \( x^{2}-2 x-3 \)

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Mar 14,2025

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Наименьшее значение выражения \(x^2 - 2x - 3\) равно \(-4\), и оно достигается при \(x = 1\).

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Щоб знайти найменше значення виразу \( x^{2}-2 x-3 \), можна використовувати метод знаходження вершини параболи. Вершина квадратичної функції задана формулою \( x = -\frac{b}{2a} \), де \( a = 1 \) і \( b = -2 \). Підставивши значення, отримуємо \( x = \frac{2}{2} = 1 \). Тепер підставимо \( x = 1 \) у вираз: \( 1^2 - 2 \cdot 1 - 3 = 1 - 2 - 3 = -4 \). Таким чином, найменше значення виразу дорівнює -4.

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