{"id":5507,"date":"2025-12-24T17:18:16","date_gmt":"2025-12-24T08:18:16","guid":{"rendered":"https:\/\/math-travel.com\/?p=5507"},"modified":"2026-03-04T08:59:20","modified_gmt":"2026-03-03T23:59:20","slug":"heikouidou","status":"publish","type":"post","link":"https:\/\/math-travel.jp\/math-1\/heikouidou\/","title":{"rendered":"2\u6b21\u95a2\u6570\u306e\u5e73\u884c\u79fb\u52d5\u516c\u5f0f\u3092\u8a3c\u660e\uff01\u306a\u305c\u300c\u30de\u30a4\u30ca\u30b9\u300d\u306b\u306a\u308b\u306e\u304b\u7406\u7531\u3092\u89e3\u8aac"},"content":{"rendered":"\n

\u4eca\u56de\u306f2\u6b21\u95a2\u6570\u306e\u5e73\u884c\u79fb\u52d5\u306b\u95a2\u3059\u308b\u60a9\u307f\u3092\u89e3\u6c7a\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

\u4eca\u56de\u89e3\u6c7a\u3059\u308b\u60a9\u307f<\/span><\/div>
\n

\u300c\u5e73\u884c\u79fb\u52d5\u306e\u516c\u5f0f\u3063\u3066\u306a\u3093\u3060\u3063\u3051\u300d <\/p>\n\n\n\n

\u300c2\u6b21\u95a2\u6570\u306e\u5e73\u884c\u79fb\u52d5\u3063\u3066\uff1f\u300d<\/p>\n<\/div><\/div>\n\n\n\n

 <\/p>\n\n\n\n

\u30b0\u30e9\u30d5\u306e\u5f62\u3092\u4e00\u5207\u5909\u3048\u308b\u3053\u3068\u306a\u304f\u79fb\u52d5\u3055\u305b\u308b\u3053\u3068\u3092\u5e73\u884c\u79fb\u52d5<\/span>\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n\n\n

\n
\"2\u6b21\u95a2\u6570\u306e\u5e73\u884c\u79fb\u52d5\"<\/figure>\n<\/div>\n\n\n
\u5e73\u884c\u79fb\u52d5\u306e\u516c\u5f0f<\/span><\/div>
\n

\\(y=ax^{2}\\)\u306e\u30b0\u30e9\u30d5\u3092\\(x\\)\u8ef8\u65b9\u5411\u306b\\(p\\)\u3001\\(y\\)\u8ef8\u65b9\u5411\u306b\\(q\\)\u3060\u3051\u5e73\u884c\u79fb\u52d5\u3055\u305b\u305f\u3082\u306e\u306f<\/p>\n\n\n\n

\\[y=a(x-p)^{2}+q\\]<\/p>\n\n\n\n

\u3068\u8868\u3057\u307e\u3059\u3002<\/p>\n<\/div><\/div>\n\n\n\n

\u672c\u8a18\u4e8b\u3067\u306f2\u6b21\u95a2\u6570\u306e\u5e73\u884c\u79fb\u52d5<\/span>\u306b\u3064\u3044\u3066\u89e3\u8aac\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

\u306a\u305c\u5e73\u884c\u79fb\u52d5\u306e\u516c\u5f0f\u3067\u306f\u7b26\u53f7\u304c\u9006\u306b\u306a\u308b\u306e\u304b\u3082\u89e3\u8aac\u3057\u3066\u3044\u308b\u306e\u3067\u3001\u305c\u3072\u6700\u5f8c\u307e\u3067\u3054\u89a7\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n

2\u6b21\u95a2\u6570\u306e\u5e73\u884c\u79fb\u52d5<\/h2>\n\n\n
\"2\u6b21\u95a2\u6570\u306e\u57fa\u672c\u5f62\u304b\u3089\u5e73\u884c\u79fb\u52d5\u5f8c\u306e\u5f0f\u3078\u306e\u5909\u5316\u3068\u3001\u9802\u70b9\u306e\u79fb\u52d5\u3092\u8996\u899a\u5316\u3057\u305f\u6982\u5ff5\u56f3\"<\/figure>\n\n\n\n\n

2\u6b21\u95a2\u6570\u306e\u5e73\u884c\u79fb\u52d5\u306b\u306f\u516c\u5f0f\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n

\n
\"2\u6b21\u95a2\u6570\u306e\u5e73\u884c\u79fb\u52d5\"<\/figure>\n<\/div>\n\n\n
\u5e73\u884c\u79fb\u52d5\u306e\u516c\u5f0f<\/span><\/div>
\n

\\(y=ax^{2}\\)\u306e\u30b0\u30e9\u30d5\u3092\\(x\\)\u8ef8\u65b9\u5411\u306b\\(p\\)\u3001\\(y\\)\u8ef8\u65b9\u5411\u306b\\(q\\)\u3060\u3051\u5e73\u884c\u79fb\u52d5\u3055\u305b\u305f\u3082\u306e\u306f<\/p>\n\n\n\n

\\(y=a(x-p)^{2}+q\\)<\/p>\n<\/div><\/div>\n\n\n\n

\\(x\\)\u8ef8\u65b9\u5411\u306b\\(p\\)\u3060\u3051\u5e73\u884c\u79fb\u52d5\u3059\u308b\u3068\u304d\u306f\u3001\\(x\\)\u3092\\(x-p\\)\u306b\u7f6e\u304d\u63db\u3048\u307e\u3059\u3002<\/p>\n\n\n\n

\u307e\u305f\u3001\\(y\\)\u8ef8\u65b9\u5411\u306b\\(q\\)\u3060\u3051\u5e73\u884c\u79fb\u52d5\u3059\u308b\u306a\u3089\u3001\\(y\\)\u3092\\(y-p\\)\u306b\u7f6e\u304d\u63db\u3048\u307e\u3059\u3002<\/p>\n\n\n\n

\u3053\u308c\u3067\\(y=ax^{2}\\)\u306e\u30b0\u30e9\u30d5\u3092\\(x\\)\u8ef8\u65b9\u5411\u306b\\(p\\)\u3001\\(y\\)\u8ef8\u65b9\u5411\u306b\\(q\\)\u3060\u3051\u5e73\u884c\u79fb\u52d5\u3055\u305b\u305f\u3082\u306e\u306f<\/p>\n\n\n\n

\\(y=a(x-p)^{2}+q\\)\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n

 <\/p>\n\n\n\n

2\u6b21\u95a2\u6570\u306e\u8ef8\u3084\u9802\u70b9\u3092\u6c42\u3081\u65b9\u3092\u77e5\u3063\u3066\u3044\u308b\u3068\u3001\u4eca\u56de\u306e\u5e73\u884c\u79fb\u52d5\u306e\u516c\u5f0f\u3082\u7406\u89e3\u3057\u3084\u3059\u304f\u306a\u308b\u3067\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

\uff1e\uff1e2\u6b21\u95a2\u6570\u306e\u9802\u70b9\u30fb\u8ef8\u3092\u5e73\u65b9\u5b8c\u6210\u3067\u6c42\u3081\u308b\u624b\u9806\u3092\u5206\u304b\u308a\u3084\u3059\u304f\u89e3\u8aac\uff01<\/p>\n\n\n

\"\"\u9ad8\u6821\u751f<\/span><\/div>
\n

\u3053\u308c\u306f\u6697\u8a18\u3059\u308b\u516c\u5f0f\u3067\u3059\u304b\uff1f<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n

\"\"\u30b7\u30fc\u30bf<\/span><\/div>
\n

\u5e73\u884c\u79fb\u52d5\u306f\u6697\u8a18\u3067\u306f\u306a\u304f\u3001\u4f7f\u3044\u65b9\u3092\u899a\u3048\u3066\u6b32\u3057\u3044\u304b\u306a\uff01
\u5177\u4f53\u4f8b\u3092\u898b\u305b\u308b\u304b\u3089\u4f7f\u3048\u308b\u3088\u3046\u306b\u3057\u3088\u3046\u3002<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

\u4f8b1\u3000\\(y=x^{2}\\)\u3092\u5e73\u884c\u79fb\u52d5<\/h3>\n\n\n
\n
\"2\u6b21\u95a2\u6570\u306e\u5e73\u884c\u79fb\u52d51\"<\/figure>\n<\/div>\n\n\n
\u4f8b\u984c\uff11<\/span><\/div>
\n

\\(y=x^{2}\\)\u3092\\(x\\)\u8ef8\u65b9\u5411\u306b\\(3\\),\\(y\\)\u8ef8\u65b9\u5411\u306b\\(2\\)\u3060\u3051\u5e73\u884c\u79fb\u52d5\u3055\u305b\u308b\u3002<\/p>\n<\/div><\/div>\n\n\n\n

\u3053\u306e\u5834\u5408\u3001\\(x\\)\u3092\\(x-3\\)\u306b\u7f6e\u304d\u63db\u3048\u3066\u3001\\(y\\)\u3092\\(y-2\\)\u306b\u7f6e\u304d\u63db\u3048\u307e\u3059\u3002<\/p>\n\n\n\n

\u30dd\u30a4\u30f3\u30c8<\/span><\/div>
\n

\\begin{eqnarray}
x &\u21d2& x-3\\\\
y &\u21d2& y-2\uff12
\\end{eqnarray}<\/p>\n<\/div><\/div>\n\n\n\n

\u3059\u308b\u3068\u3001\u5e73\u884c\u79fb\u52d5\u3057\u305f\u5f0f\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n

\\[y-2=(x-3)^{2}\\]<\/p>\n\n\n\n

\u3053\u308c\u3092\u6574\u7406\u3057\u3066\u5e73\u884c\u79fb\u52d5\u306e\u5b8c\u6210\u3067\u3059\u3002<\/p>\n\n\n\n

\\[y=(x-3)^{2}+2\\]<\/p>\n\n\n\n

\u4f8b2\u3000\\(y=-2x^{2}\\)\u3092\u5e73\u884c\u79fb\u52d5<\/h3>\n\n\n\n

\u6b21\u306f\\(x^{2}\\)\u304c\u4fc2\u6570\u3092\u6301\u3064\u5834\u5408\u3067\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n

\n
\"2\u6b21\u95a2\u6570\u306e\u5e73\u884c\u79fb\u52d52\"<\/figure>\n<\/div>\n\n\n
\u4f8b\u984c2<\/span><\/div>
\n

\\(y=-2x^{2}\\)\u3092\\(x\\)\u8ef8\u65b9\u5411\u306b\\(-2\\),\\(y\\)\u8ef8\u65b9\u5411\u306b\\(3\\)\u3060\u3051\u5e73\u884c\u79fb\u52d5\u3055\u305b\u308b\u3002<\/p>\n<\/div><\/div>\n\n\n\n

\\(x\\)\u3092\\(x+2\\)\u306b\u7f6e\u304d\u63db\u3048\u3066\u3001\\(y\\)\u3092\\(y-3\\)\u306b\u7f6e\u304d\u63db\u3048\u307e\u3059\u3002<\/p>\n\n\n\n

\u30dd\u30a4\u30f3\u30c8<\/span><\/div>
\n

\\begin{eqnarray}
x &\u21d2&x+3\\\\
y &\u21d2&y-3
\\end{eqnarray}<\/p>\n<\/div><\/div>\n\n\n\n

\\[y-3=-2(x+2)^{2}\\]<\/p>\n\n\n\n

\u3053\u308c\u3092\u6574\u7406\u3057\u3066\u3001<\/p>\n\n\n\n

\\[y=-2(x+2)^{2}+3\\]<\/p>\n\n\n\n

\u4f8b3\u3000\\(y=x^{2}+6x+4\\)\u3092\u5e73\u884c\u79fb\u52d5<\/h3>\n\n\n\n

\u6700\u5f8c\u306b\u3053\u3093\u306a\u554f\u984c\u3082\u7528\u610f\u3057\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

\u4f8b\u984c3<\/span><\/div>
\n

\\(y=x^{2}+6x+4\\)\u3092\\(x\\)\u8ef8\u65b9\u5411\u306b\\(-2\\),\\(y\\)\u8ef8\u65b9\u5411\u306b\\(3\\)\u3060\u3051\u5e73\u884c\u79fb\u52d5\u3055\u305b\u308b\u3002<\/p>\n<\/div><\/div>\n\n\n\n

\u3053\u306e\u3068\u304d\u3001\\(y=x^{2}+6x+4\\)\u3092\u5e73\u884c\u79fb\u52d5\u3055\u305b\u308b\u65b9\u6cd5\u304c\uff12\u3064\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n

\n
    \n
  1. \u305d\u306e\u307e\u307e\u5e73\u884c\u79fb\u52d5<\/li>\n\n\n\n
  2. \u5e73\u65b9\u5b8c\u6210\u3057\u3066\u304b\u3089\u5e73\u884c\u79fb\u52d5<\/li>\n<\/ol>\n<\/div><\/div>\n\n\n\n

    \u65b9\u6cd51.\u305d\u306e\u307e\u307e\u5e73\u884c\u79fb\u52d5<\/h4>\n\n\n\n

    \\(x\\)\u8ef8\u65b9\u5411\u306b\\(-2\\),\\(y\\)\u8ef8\u65b9\u5411\u306b\\(3\\)\u3060\u3051\u5e73\u884c\u79fb\u52d5\u3059\u308b\u306e\u3067\u3001<\/p>\n\n\n\n

    \\begin{eqnarray}
    \ny-3&=&(x+2)^{2}+6(x+2)+4\\\\
    \ny&=&(x^{2}+4x+4)+6(x+2)+4+3\\\\
    \ny&=&x^{2}+10x+23
    \n\\end{eqnarray}<\/p>\n\n\n\n

    \u3057\u305f\u304c\u3063\u3066\u3001\u6c42\u3081\u308b2\u6b21\u95a2\u6570\u306f<\/p>\n\n\n\n

    \\[y=x^{2}+10x+23\\]<\/p>\n\n\n\n

    \u3060\u3068\u5206\u304b\u308a\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

    \u65b9\u6cd52.\u5e73\u65b9\u5b8c\u6210\u3057\u3066\u304b\u3089\u5e73\u884c\u79fb\u52d5<\/h4>\n\n\n\n

    \u3082\u3046\uff11\u3064\u306e\u3084\u308a\u65b9\u3068\u3057\u3066\u3001\u5e73\u65b9\u5b8c\u6210\u3057\u3066\u304b\u3089\u79fb\u52d5\u3059\u308b\u65b9\u6cd5\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

    \u307e\u305a\u306f\\(y=x^{2}+6x+4\\)\u3092\u5e73\u65b9\u5b8c\u6210\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

    \\begin{eqnarray*}
    \ny&=&x^{2}+6x+4\\\\
    \n&=&(x+3)^{2}-9+4\\\\
    \n&=&(x+3)^{2}-5
    \n\\end{eqnarray*}<\/p>\n\n\n\n

    \u3053\u306e\u95a2\u6570\u304c\\(x\\)\u8ef8\u65b9\u5411\u306b\\(-2\\),\\(y\\)\u8ef8\u65b9\u5411\u306b\\(3\\)\u3060\u3051\u5e73\u884c\u79fb\u52d5\u3059\u308b\u306e\u3067<\/p>\n\n\n\n

    \\(x\\)\u3092\\(x+2\\)\u306b\u7f6e\u304d\u63db\u3048\u3066\u3001\\(y\\)\u3092\\(y-3\\)\u306b\u7f6e\u304d\u63db\u3048\u307e\u3059\u3002<\/p>\n\n\n\n

    \\begin{eqnarray*}
    \ny-3&=&(x+2+3)^{2}-5\\\\
    \n&=&(x+5)^{2}-5+3\\\\
    \n&=&x^{2}+10x+23
    \n\\end{eqnarray*}<\/p>\n\n\n\n

    \u3057\u305f\u304c\u3063\u3066\u3001\u6c42\u3081\u308b2\u6b21\u95a2\u6570\u306f<\/p>\n\n\n\n

    \\[y=x^{2}+10x+23\\]<\/p>\n\n\n\n

    \u3068\u306a\u308a\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

    2\u3064\u306e\u3084\u308a\u65b9\u3092\u7d39\u4ecb\u3057\u307e\u3057\u305f\u304c\u3001\u3069\u3061\u3089\u306e\u3084\u308a\u65b9\u3067\u3082\u540c\u3058\u5f0f\u306b\u306a\u308b\u306e\u3067\u5b89\u5fc3\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n

    \"\"\u9ad8\u6821\u751f<\/span><\/div>
    \n

    \u5e73\u884c\u79fb\u52d5\u306e\u3084\u308a\u65b9\u304c\u5206\u304b\u3063\u3066\u304d\u307e\u3057\u305f\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

    \u306a\u305c\u7b26\u53f7\u304c\u9006\u306b\u306a\u308b\uff1f<\/h2>\n\n\n
    \"\u5e73\u884c\u79fb\u52d5\u306e\u516c\u5f0f\u3067\u7b26\u53f7\u304c\u30de\u30a4\u30ca\u30b9\u306b\u306a\u308b\u7406\u7531\u3092\u3001\u5ea7\u6a19\u306e\u9006\u7b97\u30d7\u30ed\u30bb\u30b9\u3067\u793a\u3057\u305f\u89e3\u8aac\u56f3\"<\/figure>\n\n\n\n
    \"\"\u9ad8\u6821\u751f<\/span><\/div>
    \n

    \u3069\u3046\u3057\u3066(x)\u8ef8\u65b9\u5411\u306b(p)\u79fb\u52d5\u3055\u305b\u308b\u306e\u306b\u3001(x-p)\u304c\u51fa\u3066\u304f\u308b\u306e\uff1f<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n

    \"\"\u30b7\u30fc\u30bf<\/span><\/div>
    \n

    \u3044\u3044\u8cea\u554f\u3060\u306d\uff01\u306a\u305c\u305d\u3046\u306a\u308b\u306e\u304b\u89e3\u8aac\u3059\u308b\u3088\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

     <\/p>\n\n\n\n

    \\(x\\)\u8ef8\u65b9\u5411\u306b\\(p\\)\u3060\u3051\u5e73\u884c\u79fb\u52d5\u3057\u305f\u3068\u304d\u306b\u3001\u306a\u305c\\(x-p\\)\u306b\u306a\u308b\u306e\u304b\u7591\u554f\u306b\u601d\u3046\u65b9\u3082\u591a\u3044\u306f\u305a\u3002<\/p>\n\n\n\n

    \u3072\u3087\u3063\u3068\u3059\u308b\u3068\u3001<\/p>\n\n\n\n

    \u300c\\(p\\)\u3060\u3051\u5e73\u884c\u79fb\u52d5\u3057\u305f\u304b\u3089\u3001\\(x+p\\)\u306e\u307b\u3046\u304c\u7d0d\u5f97\u3067\u304d\u308b\u3093\u3060\u3051\u3069…\u300d<\/p>\n\n\n\n

    \u3053\u3093\u306a\u4eba\u3082\u3044\u308b\u306e\u3067\u306f\u306a\u3044\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n\n\n\n

     <\/p>\n\n\n\n

    \u25bd\u3053\u3053\u3067\u306f\u7b26\u53f7\u304c\u9006\u306b\u306a\u308b\u3053\u3068\u3092\u89e3\u8aac\u3057\u307e\u3059\u3002<\/span><\/p>\n\n\n\n

    \\(y=ax^{2}\\)\u306e\u30b0\u30e9\u30d5\u3092\\(x\\)\u8ef8\u65b9\u5411\u306b\\(p\\)\u3001\\(y\\)\u8ef8\u65b9\u5411\u306b\\(q\\)\u3060\u3051\u5e73\u884c\u79fb\u52d5\u3055\u305b\u305f\u3082\u306e\u306f<\/p>\n\n\n\n

    \\[y=a(x-p)^{2}+q\\]<\/p>\n\n\n\n

    \u3067\u3057\u305f\u306d\u3002<\/p>\n\n\n\n

     <\/p>\n\n\n\n

    \u3053\u3053\u306b2\u6b21\u95a2\u6570\\(y=f(x)\\)\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n

    \n
    \"\u306a\u305c\u7b26\u53f7\u304c\u9006\u306b\u306a\u308b\u306e\uff1f\"<\/figure>\n<\/div>\n\n\n

    \\(y=f(x)\\)\u306e\u30b0\u30e9\u30d5\u3092\\(x\\)\u8ef8\u65b9\u5411\u306b\\(p\\)\u3001\\(y\\)\u8ef8\u65b9\u5411\u306b\\(q\\)\u3060\u3051\u5e73\u884c\u79fb\u52d5\u3055\u305b\u305f\u3082\u306e\u3092\\(y=g(x)\\)\u3068\u3057\u307e\u3059\u3002<\/p>\n\n\n

    \n
    \"\u306a\u305c\u7b26\u53f7\u304c\u9006\u306b\u306a\u308b\u306e\uff1f\uff11\"<\/figure>\n<\/div>\n\n\n

    \u3053\u306e\u3068\u304d\\(y=f(x)\\)\u4e0a\u306e\u3068\u3042\u308b\u70b9\\((x,y)\\)\u306f\u3001\\(y=g(x)\\)\u4e0a\u306e\\((X,Y)\\)\u3078\u5e73\u884c\u79fb\u52d5\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

    \u3064\u307e\u308a\u3001\u4ee5\u4e0b\u306e2\u3064\u304c\u6210\u308a\u7acb\u3063\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

    \n

    \\[X=x+p\\]<\/p>\n\n\n\n

    \\[Y=y+q\\]<\/p>\n<\/div><\/div>\n\n\n

    \n
    \"\u306a\u305c\u7b26\u53f7\u304c\u9006\u306b\u306a\u308b\u306e\uff1f2\"<\/figure>\n<\/div>\n\n\n

    \u3053\u308c\u306f\u5f0f\u5909\u5f62\u3092\u3059\u308b\u3068<\/p>\n\n\n\n

    \\begin{eqnarray}
    \nx &=& X-p\\\\
    \ny &=& Y-q
    \n\\end{eqnarray}<\/p>\n\n\n\n

    \u3068\u306a\u308a\u307e\u3059\u306d\u3002<\/p>\n\n\n\n

    \u3057\u305f\u304c\u3063\u3066\u3001\u5143\u306e2\u6b21\u95a2\u6570\\(y=f(x)\\)\u306b\u4ee3\u5165\u3059\u308b\u3068<\/p>\n\n\n\n

    \\[Y-q=f(X-p)\\]<\/p>\n\n\n\n

    \u3068\u306a\u308a\u3001<\/p>\n\n\n\n

    \\[y=f(x-p)+q\\]<\/p>\n\n\n\n

    \u304c\u6210\u7acb\u3057\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

    \u3057\u305f\u304c\u3063\u3066\u3001\\(x\\)\u8ef8\u65b9\u5411\u306b\\(p\\)\u3060\u3051\u5e73\u884c\u79fb\u52d5\u3068\u304d\u3001\\(x\\)\u306e\u90e8\u5206\u306b\u306f\\(x-p\\)\u304c\u4ee3\u5165\u3055\u308c\u3066\u3044\u308b\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059\u3002<\/p>\n\n\n\n

    \u96e3\u3057\u3044\u8a71\u306a\u306e\u3067\u3088\u304f\u5206\u304b\u3089\u306a\u3044\u65b9\u306f\u3001\u516c\u5f0f\u3060\u3051\u899a\u3048\u3066\u304a\u3051\u3070\u5927\u4e08\u592b\u3067\u3059\u3002<\/span><\/p>\n\n\n\n

    \u5e73\u884c\u79fb\u52d5\u300a\u7df4\u7fd2\u554f\u984c\u300b<\/h2>\n\n\n\n

    2\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u3092\u5e73\u884c\u79fb\u52d5\u3055\u305b\u308b\u7df4\u7fd2\u3092\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

    \u4eca\u56de\u306f\u4ee5\u4e0b\u306e3\u3064\u306e\u5f0f\u3092\u5e73\u884c\u79fb\u52d5\u3057\u3066\u3082\u3089\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

    \u7df4\u7fd2\u554f\u984c<\/span><\/div>
    \n

    \u6b21\u306e2\u6b21\u95a2\u6570\u3092\\(x\\)\u8ef8\u65b9\u5411\u306b3\u3001y\u8ef8\u65b9\u5411\u306b-2\u3060\u3051\u5e73\u884c\u79fb\u52d5\u3055\u305b\u305f\u3082\u306e\u3092\u6c42\u3081\u3088\u3046\u3002<\/p>\n\n\n\n

      \n
    • \\(y=x^{2}\\)<\/li>\n\n\n\n
    • \\(y=-2x^{2}\\)<\/li>\n\n\n\n
    • \\(y=x^{2}+x+1\\)<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n

      \\(y=x^{2}\\)\u306e\u5e73\u884c\u79fb\u52d5<\/p>\n\n\n\n

      \\(y=x^{2}\\)\u3092\\(x\\)\u8ef8\u65b9\u5411\u306b3\u3001y\u8ef8\u65b9\u5411\u306b-2\u3060\u3051\u5e73\u884c\u79fb\u52d5\u3055\u305b\u308b\u3068\u3001<\/p>\n\n\n\n

      \\begin{eqnarray*}
      \ny&=&(x-3)^{2}-2\\\\
      \n&=&(x^{2}-6x+9)-2\\\\
      \n&=&x^{2}-6x+7
      \n\\end{eqnarray*}<\/p>\n\n\n\n

      \u3057\u305f\u304c\u3063\u3066\u3001\u6c42\u3081\u308b2\u6b21\u95a2\u6570\u306f\\(y=x^{2}-6x+7\\)<\/p>\n\n\n\n

      \\(y=-2x^{2}\\)\u306e\u5e73\u884c\u79fb\u52d5<\/p>\n\n\n\n

      \\(y=-2x^{2}\\)\u3092\\(x\\)\u8ef8\u65b9\u5411\u306b3\u3001y\u8ef8\u65b9\u5411\u306b-2\u3060\u3051\u5e73\u884c\u79fb\u52d5\u3055\u305b\u308b\u3068\u3001<\/p>\n\n\n\n

      \\begin{eqnarray*}
      \ny&=&-2(x-3)^{2}-2\\\\
      \n&=&-2(x^{2}-6x+9)-2\\\\
      \n&=&-2x^{2}+12x-20
      \n\\end{eqnarray*}<\/p>\n\n\n\n

      \u3057\u305f\u304c\u3063\u3066\u3001\u6c42\u3081\u308b2\u6b21\u95a2\u6570\u306f\\(y=-2x^{2}+12x-20\\)<\/p>\n\n\n\n

      \\(y=x^{2}+x+1\\)\u306e\u5e73\u884c\u79fb\u52d5<\/p>\n\n\n\n

      \\(y=x^{2}+x+1\\)\u3092\\(x\\)\u8ef8\u65b9\u5411\u306b3\u3001y\u8ef8\u65b9\u5411\u306b-2\u3060\u3051\u5e73\u884c\u79fb\u52d5\u3055\u305b\u308b\u3068\u3001<\/p>\n\n\n\n

      \\begin{eqnarray*}
      \ny&=&(x-3)^{2}+(x-3)+1-2\\\\
      \n&=&(x^{2}-6x+9)+(x-3)-1\\\\
      \n&=&x^{2}-5x+5
      \n\\end{eqnarray*}<\/p>\n\n\n\n

      \u3057\u305f\u304c\u3063\u3066\u3001\u6c42\u3081\u308b2\u6b21\u95a2\u6570\u306f\\(y=x^{2}-5x+5\\)<\/p>\n\n\n

      \"\"\u9ad8\u6821\u751f<\/span><\/div>
      \n

      \u304a\u304b\u3052\u3067\u5c11\u3057\u6163\u308c\u3066\u304d\u307e\u3057\u305f\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

      2\u6b21\u95a2\u6570\u306e\u5e73\u884c\u79fb\u52d5\u3000\u307e\u3068\u3081<\/h2>\n\n\n
      \"2\u6b21\u95a2\u6570\u306e\u5e73\u884c\u79fb\u52d5\u306b\u304a\u3051\u308b\u7f6e\u304d\u63db\u3048\u30eb\u30fc\u30eb\u3092\u7c21\u6f54\u306b\u307e\u3068\u3081\u305f\u6bd4\u8f03\u56f3\u89e3\"<\/figure>\n\n\n\n\n

      \u4eca\u56de\u306f2\u6b21\u95a2\u6570\u306e\u5e73\u884c\u79fb\u52d5\u306e\u516c\u5f0f\u306b\u3064\u3044\u3066\u307e\u3068\u3081\u307e\u3057\u305f\u3002<\/span><\/p>\n\n\n\n

      \n
      \n

      \u5e73\u884c\u79fb\u52d5\u3057\u305f\u3044\u5f0f\u3092\u5165\u529b\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n <\/div>\n

      \n
      \n \n