二次関数の最大値または最小値を簡単に見つける方法

放物線の頂点の縦座標値（通常は k で表される）は、二次関数の最大値または最小値です。その価値を見つける方法を学びましょう！

ステップ

y = ax ² + bx + c

1. 1 最大値と最小値のどちらを探しているのかを決定します。両方を同時に見つけることはできません。どちらか一方しか見つけることができません。
   • 二次関数の最大値は頂点で発生します。 y = ax ² + bx + cの場合、 (c - b ² /4a)は頂点における関数値です。 {"smallUrl":"https:\/\/www.wikihow.com\/images_en\/thumb\/2\/26\/Find-the-Maximum-or-Minimum-Value-of-a-Quadratic-Function-Easily-Step-1Bullet1.jpg\/v4-460px-Find-the-Maximum-or-Minimum-Value-of-a-Quadratic-Function-Easily-Step-1Bullet1.jpg","bigUrl":"https:\/\/www.wikihow.com\/i mages\/thumb\/2\/26\/Find-the-Maximum-or-Minimum-Value-of-a-Quadratic-Function-Easily-Step-1Bullet1.jpg\/v4-728px-Find-the-Maximum-or-Minimum-Value-of-a-Quadratic-Function-Easily-Step-1Bullet1.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"}
   • aが正の場合: 放物線が上向きに開くため、最小値が得られます。 （頂点は最も低い点です） {"smallUrl":"https:\/\/www.wikihow.com\/images_en\/thumb\/d\/da\/Find-the-Maximum-or-Minimum-Value-of-a-Quadratic-Function-Easily-Step-1Bullet2.jpg\/v4-460px-Find-the-Maximum-or-Minimum-Value-of-a-Quadratic-Function-Easily-Step-1Bullet2.jpg","bigUrl":"https:\/\/www.wikihow.com\/i mages\/thumb\/d\/da\/Find-the-Maximum-or-Minimum-Value-of-a-Quadratic-Function-Easily-Step-1Bullet2.jpg\/v4-728px-Find-the-Maximum-or-Minimum-Value-of-a-Quadratic-Function-Easily-Step-1Bullet2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"}
   • aが負の場合: 放物線が下向きに開くため (頂点が最高点となるため)、最大値が得られます。 {"smallUrl":"https:\/\/www.wikihow.com\/images_en\/thumb\/7\/70\/Find-the-Maximum-or-Minimum-Value-of-a-Quadratic-Function-Easily-Step-1Bullet3.jpg\/v4-460px-Find-the-Maximum-or-Minimum-Value-of-a-Quadratic-Function-Easily-Step-1Bullet3.jpg","bigUrl":"https:\/\/www.wikihow.com\/i mages\/thumb\/7\/70\/Find-the-Maximum-or-Minimum-Value-of-a-Quadratic-Function-Easily-Step-1Bullet3.jpg\/v4-728px-Find-the-Maximum-or-Minimum-Value-of-a-Quadratic-Function-Easily-Step-1Bullet3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"}
   • aの値が 0 の場合、それは二次関数ではなく、ここでの議論の範囲外となります。 {"smallUrl":"https:\/\/www.wikihow.com\/images_en\/thumb\/8\/8f\/Find-the-Maximum-or-Minimum-Value-of-a-Quadratic-Function-Easily-Step-1Bullet4.jpg\/v4-460px-Find-the-Maximum-or-Minimum-Value-of-a-Quadratic-Function-Easily-Step-1Bullet4.jpg","bigUrl":"https:\/\/www.wikihow.com\/i mages\/thumb\/8\/8f\/Find-the-Maximum-or-Minimum-Value-of-a-Quadratic-Function-Easily-Step-1Bullet4.jpg\/v4-728px-Find-the-Maximum-or-Minimum-Value-of-a-Quadratic-Function-Easily-Step-1Bullet4.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"}
   広告する

y = a(xh) ² + k 形式

1. {"smallUrl":"https:\/\/www.wikihow.com\/images_en\/thumb\/1\/11\/Find-the-Maximum-or-Minimum-Value-of-a-Quadratic-Function-Easily-Step-2.jpg\/v4-460px-Find-the-Maximum-or-Minimum-Value-of-a-Quadratic-Function-Easily-Step-2.jpg","bigUrl":"https:\/\/www.wikihow.com\/i mages\/thumb\/1\/11\/Find-the-Maximum-or-Minimum-Value-of-a-Quadratic-Function-Easily-Step-2.jpg\/v4-728px-Find-the-Maximum-or-Minimum-Value-of-a-Quadratic-Function-Easily-Step-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 1y = a(xh) ² + k の場合、 k は頂点における関数の最大値です。
   • kは二次関数の最大値または最小値であり、 aが正か負かに応じて変化します。 {"smallUrl":"https:\/\/www.wikihow.com\/images_en\/thumb\/4\/4d\/Find-the-Maximum-or-Minimum-Value-of-a-Quadratic-Function-Easily-Step-2Bullet1.jpg\/v4-460px-Find-the-Maximum-or-Minimum-Value-of-a-Quadratic-Function-Easily-Step-2Bullet1.jpg","bigUrl":"https:\/\/www.wikihow.com\/i mages\/thumb\/4\/4d\/Find-the-Maximum-or-Minimum-Value-of-a-Quadratic-Function-Easily-Step-2Bullet1.jpg\/v4-728px-Find-the-Maximum-or-Minimum-Value-of-a-Quadratic-Function-Easily-Step-2Bullet1.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"}

例

1. {"smallUrl":"https:\/\/www.wikihow.com\/images_en\/thumb\/c\/c4\/Find-the-Maximum-or-Minimum-Value-of-a-Quadratic-Function-Easily-Step-3.jpg\/v4-460px-Find-the-Maximum-or-Minimum-Value-of-a-Quadratic-Function-Easily-Step-3.jpg","bigUrl":"https:\/\/www.wikihow.com\/i mages\/thumb\/c\/c4\/Find-the-Maximum-or-Minimum-Value-of-a-Quadratic-Function-Easily-Step-3.jpg\/v4-728px-Find-the-Maximum-or-Minimum-Value-of-a-Quadratic-Function-Easily-Step-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 1この関数の最大値または最小値を見つけます: f(x) = x ² + x + 1
2. {"smallUrl":"https:\/\/www.wikihow.com\/images_en\/thumb\/c\/c9\/Find-the-Maximum-or-Minimum-Value-of-a-Quadratic-Function-Easily-Step-4.jpg\/v4-460px-Find-the-Maximum-or-Minimum-Value-of-a-Quadratic-Function-Easily-Step-4.jpg","bigUrl":"https:\/\/www.wikihow.com\/i mages\/thumb\/c\/c9\/Find-the-Maximum-or-Minimum-Value-of-a-Quadratic-Function-Easily-Step-4.jpg\/v4-728px-Find-the-Maximum-or-Minimum-Value-of-a-Quadratic-Function-Easily-Step-4.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 2この関数の最大値または最小値を見つけます: f(x) = -2(x-1) ² + 3広告

ヒント

• 放物線の対称軸はx = hである。
• -h は、最大値が得られたときの独立変数の値です。