{"id":5451,"date":"2025-12-24T17:18:16","date_gmt":"2025-12-24T08:18:16","guid":{"rendered":"https:\/\/math-travel.com\/?p=5451"},"modified":"2026-02-11T16:07:13","modified_gmt":"2026-02-11T07:07:13","slug":"quadratic-graph","status":"publish","type":"post","link":"https:\/\/math-travel.jp\/math-1\/quadratic-graph\/","title":{"rendered":"\u4e8c\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306e\u66f8\u304d\u65b9\u30103\u30b9\u30c6\u30c3\u30d7\u3011\u3067\u8ab0\u3067\u3082\u8ff7\u308f\u305a\u66f8\u3051\u308b\u624b\u9806\u3092\u516c\u958b"},"content":{"rendered":"\n

\u6570\u5b66\u2160\u306e\u4e8c\u6b21\u95a2\u6570\u3067\u306f\u30b0\u30e9\u30d5\u304c\u5fc5\u8981\u306a\u554f\u984c<\/span>\u304c\u305f\u304f\u3055\u3093\u3042\u308a\u307e\u3059\u3002<\/span><\/p>\n\n\n\n

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

\u300c2\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u3063\u3066\u3069\u3093\u306a\u5f62\u300d <\/p>\n\n\n\n

\u300c\u30b0\u30e9\u30d5\u306e\u66f8\u304d\u65b9\u304c\u5206\u304b\u3089\u306a\u3044\u300d<\/p>\n<\/div><\/div>\n\n\n\n

\u4eca\u56de\u306f2\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306b\u95a2\u3059\u308b\u3053\u3093\u306a\u60a9\u307f\u3092\u89e3\u6c7a\u3057\u307e\u3059\u3002<\/p>\n\n\n

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

2\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u3092\u66f8\u304d\u305f\u3044\u3093\u3060\u3051\u3069\u3001\u66f8\u304d\u65b9\u304c\u5206\u304b\u3089\u306a\u304f\u3066\u2026<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n

\n
\"2\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306e\u66f8\u304d\u65b9\"<\/figure>\n<\/div>\n\n\n

2\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306f\u4ee5\u4e0b\u306e3\u30b9\u30c6\u30c3\u30d7<\/span>\u3067\u66f8\u304f\u3068\u4e0a\u624b\u306b\u63cf\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n

\u30b0\u30e9\u30d5\u3092\u66f8\u304f\u624b\u9806<\/span><\/div>
\n
    \n
  1. \u9802\u70b9\u3092\u6c42\u3081\u308b<\/li>\n\n\n\n
  2. y\u8ef8\u3068\u306e\u4ea4\u70b9\u3092\u6c42\u3081\u308b<\/li>\n\n\n\n
  3. \u9802\u70b9\u3068y\u8ef8\u3068\u306e\u4ea4\u70b9\u3092\u306a\u3081\u3089\u304b\u306b\u7d50\u3076<\/li>\n<\/ol>\n<\/div><\/div>\n\n\n\n

    \u672c\u8a18\u4e8b\u3067\u306f2\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306e\u66f8\u304d\u65b9\u3092\u89e3\u8aac<\/span>\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n\n\n\n

    \u5177\u4f53\u4f8b\u3092\u7528\u610f\u3057\u305f\u306e\u3067\u3058\u3063\u304f\u308a\u3068\u8aad\u3093\u3067\u3082\u3089\u3048\u3070\u30012\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u304c\u66f8\u3051\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n

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

    \u6c17\u306b\u306a\u308b\u898b\u51fa\u3057\u3092\u30af\u30ea\u30c3\u30af\u3057\u3066\u3001
    \u305c\u3072\u6700\u5f8c\u307e\u3067\u3054\u89a7\u304f\u3060\u3055\u3044\u3002<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

    2\u6b21\u95a2\u6570\u306e\u57fa\u790e<\/h2>\n\n\n\n

    2\u6b21\u95a2\u6570\\(y=ax^{2}+bx+c\\)\u306e\u30b0\u30e9\u30d5\u306f\u3053\u3093\u306a\u5f62\u3092\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n

    \n
    \"2\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\"<\/figure>\n<\/div>\n\n\n

    \u95a2\u6570\\(y=ax^{2}+bx+c\\)\u306e\u4e2d\u3067\u6700\u3082\u6b21\u6570\u304c\u9ad8\u3044\u9805\u306f\\(ax^{2}\\)\u3067\u3059\u306d\u3002\u6700\u9ad8\u6b21\u6570\u304c2\u306a\u306e\u30672\u6b21\u95a2\u6570<\/span>\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

    \\(y=ax+b\\)\u306e\u5834\u5408\u3001\u6700\u3082\u6b21\u6570\u304c\u9ad8\u3044\u9805\u304c\\(ax\\)\u3067\u6b21\u65701\u306a\u306e\u3067\u4e00\u6b21\u95a2\u6570\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

    \u53c2\u8003<\/span><\/div>
    \n

    \\(y=ax^{3}+bx^{2}+cx+d\\)\u306f\u4e09\u6b21\u95a2\u6570<\/p>\n\n\n\n

    \\(y=ax^{4}+bx^{3}+cx^{2}+dx+e\\)\u306f\u56db\u6b21\u95a2\u6570<\/p>\n<\/div><\/div>\n\n\n\n

    2\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306e\u5f62<\/h2>\n\n\n\n

    2\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306f\u5de6\u53f3\u5bfe\u79f0\u306a\u653e\u7269\u7dda\u3092\u63cf\u304d\u307e\u3059\u3002<\/p>\n\n\n

    \n
    \"2\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\"<\/figure>\n<\/div>\n\n\n

    \\(y=ax^{2}+bx+c\\)\u306e\u30b0\u30e9\u30d5\u306f\\(a\\)\u306e\u7b26\u53f7\u306b\u3088\u3063\u3066\u5f62\u304c\u5909\u308f\u308a\u307e\u3059\u3002<\/span><\/p>\n\n\n\n

    2\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306e\u5f62<\/span><\/div>
    \n

    \\(a>0\\)\u306e\u3068\u304d\u3001\u4e0b\u5411\u304d\u306b\u51f8\u306a\u653e\u7269\u7dda<\/p>\n\n\n\n

    \\(a<0\\)\u306e\u3068\u304d\u3001\u4e0a\u5411\u304d\u306b\u51f8\u306a\u653e\u7269\u7dda<\/p>\n<\/div><\/div>\n\n\n\n

    \\(a>0\\)\u306e\u3068\u304d\u3001\u4e0b\u5411\u304d\u306b\u51f8\u306a\u653e\u7269\u7dda<\/h3>\n\n\n\n

    2\u6b21\u95a2\u6570\\(y=ax^{2}+bx+c\\)\u306b\u304a\u3044\u3066\\(a\\)\u304c\u6b63\u306e\u6570\u306a\u3089\u3070\u3001\u30b0\u30e9\u30d5\u306f\u4e0b\u5411\u304d\u306b\u51f8\u306a\u653e\u7269\u7dda<\/span>\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n

    \n
    \"2\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306e\u5f62\"<\/figure>\n<\/div>\n\n\n
    \u4f8b<\/span><\/div>
    \n

    \\[y=x^{2}-3x+5\\]<\/p>\n\n\n\n

    \\[y=3x^{2}-4x+4\\]<\/p>\n<\/div><\/div>\n\n\n\n

    \\(a<0\\)\u306e\u3068\u304d\u3001\u4e0a\u5411\u304d\u306b\u51f8\u306a\u653e\u7269\u7dda<\/h3>\n\n\n\n

    2\u6b21\u95a2\u6570\\(y=ax^{2}+bx+c\\)\u306b\u304a\u3044\u3066\\(a\\)\u304c\u8ca0\u306e\u6570\u306a\u3089\u3070\u3001\u30b0\u30e9\u30d5\u306f\u4e0a\u5411\u304d\u306b\u51f8\u306a\u653e\u7269\u7dda<\/span>\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n

    \n
    \"2\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306e\u5f621\"<\/figure>\n<\/div>\n\n\n
    \u4f8b<\/span><\/div>
    \n

    \\[y=-x^{2}+3x-5\\]<\/p>\n\n\n\n

    \\[y=-3x^{2}+4x-4\\]<\/p>\n<\/div><\/div>\n\n\n

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

    \u30b0\u30e9\u30d5\u306e\u5f62\u306f\u7406\u89e3\u3067\u304d\u307e\u3057\u305f\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

    2\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306e\u66f8\u304d\u65b9<\/h2>\n\n\n
    \n
    \"2\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306e\u66f8\u304d\u65b9\"<\/figure>\n<\/div>\n\n\n

    2\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306f\u4ee5\u4e0b\u306e3\u30b9\u30c6\u30c3\u30d7\u3067\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n

    \u30b0\u30e9\u30d5\u3092\u66f8\u304f\u624b\u9806<\/span><\/div>
    \n
      \n
    1. \u9802\u70b9\u3092\u6c42\u3081\u308b<\/li>\n\n\n\n
    2. y\u8ef8\u3068\u306e\u4ea4\u70b9\u3092\u6c42\u3081\u308b<\/li>\n\n\n\n
    3. \u9802\u70b9\u3068y\u8ef8\u3068\u306e\u4ea4\u70b9\u3092\u7d50\u3076<\/li>\n<\/ol>\n<\/div><\/div>\n\n\n\n

      \\(y=x^{2}+6x+5\\)\u3092\u4f8b\u306b\u3057\u3066\u5404\u30b9\u30c6\u30c3\u30d7\u3092\u8a73\u3057\u304f\u89e3\u8aac\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

      STEP1\u30b0\u30e9\u30d5\u306e\u9802\u70b9\u3092\u6c42\u3081\u308b<\/p>\n\n\n\n

      \u307e\u305a\u306f\u9802\u70b9\u306e\u5ea7\u6a19\u3092\u6c42\u3081\u307e\u3059\u3002<\/p>\n\n\n\n

      \uff12\u6b21\u95a2\u6570\u306e\u9802\u70b9\u306f\u95a2\u6570\u3092\u5e73\u65b9\u5b8c\u6210<\/span>\u3059\u308b\u3053\u3068\u3067\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n

      2\u6b21\u95a2\u6570\u306e\u8ef8\u3068\u9802\u70b9<\/span><\/div>
      \n

      \\(y=a(x+p)^{2}+q\\)\u306e\u3068\u304d\u3001<\/p>\n\n\n\n

      \u8ef8\uff1a\\(x=-p\\)  \u3001\u9802\u70b9\\((-p,q)\\)<\/p>\n<\/div><\/div>\n\n\n\n

      \u4f8b\u3068\u3057\u3066\\(y=x^{2}+6x+5\\)\u3092\u5e73\u65b9\u5b8c\u6210\u3059\u308b\u3068<\/p>\n\n\n\n

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

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

      \u3057\u305f\u304c\u3063\u3066\u3001\\(y=x^{2}+6x+5\\)\u306e\u9802\u70b9\u306f\\((-3,-4)\\)\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n

      \n
      \"2\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306e\u66f8\u304d\u65b9\"<\/figure>\n<\/div>\n\n\n

      STEP2y\u8ef8\u3068\u306e\u4ea4\u70b9\u3092\u6c42\u3081\u308b<\/p>\n\n\n\n

      \u9802\u70b9\u306e\u5ea7\u6a19\u304c\u5206\u304b\u3063\u305f\u3060\u3051\u3067\u306f\uff12\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u3092\u66f8\u304f\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002<\/p>\n\n\n\n

      \u6b21\u306f\u30b0\u30e9\u30d5\u3068y\u8ef8\u3068\u306e\u4ea4\u70b9\u3092\u6c42\u3081\u307e\u3059\u3002<\/p>\n\n\n\n

      y\u8ef8\u3068\u306e\u4ea4\u70b9\u306e\u6c42\u3081\u65b9<\/span><\/div>
      \n

      y\u8ef8\u3068\u306e\u4ea4\u70b9\u3092\u6c42\u3081\u308b \u21d2 \u95a2\u6570\u306b\\(x=0\\)\u3092\u4ee3\u5165<\/p>\n<\/div><\/div>\n\n\n\n

      y\u8ef8\u4e0a\u306e\u70b9\u3068\u3044\u3046\u3053\u3068\u306f\u3001\u70b9\u306ex\u5ea7\u6a19\u304c0\u3067\u3042\u308b\u3053\u3068\u3092\u6307\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

      \\(y=x^{2}+6x+5\\)\u306b\\(x=0\\)\u3092\u4ee3\u5165\u3059\u308b\u3068<\/p>\n\n\n\n

      \\begin{eqnarray*}
      y&=&0^{2}+6 \\cdot 0+5\\\\
      &=&5
      \\end{eqnarray*}<\/p>\n\n\n\n

      \u3057\u305f\u304c\u3063\u3066\u3001<\/p>\n\n\n\n

      \\(y=x^{2}+6x+5\\)\u306e\u30b0\u30e9\u30d5\u306f\\((0,5)\\)\u3067y\u8ef8\u3068\u4ea4\u308f\u308b\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

      STEP3\u9802\u70b9\u3068y\u8ef8\u306e\u4ea4\u70b9\u3092\u6ed1\u3089\u304b\u306b\u3064\u306a\u3050<\/p>\n\n\n\n

      \u6700\u5f8c\u306bSTEP1,2\u3067\u6c42\u3081\u305f\u9802\u70b9\u3068y\u8ef8\u3068\u306e\u4ea4\u70b9\u3092\u6ed1\u3089\u304b\u306b\u3064\u306a\u304e\u307e\u3059\u3002<\/p>\n\n\n\n

      \\(y=x^{2}+6x+5\\)\u306e\u9802\u70b9\u306f\\((-3,-4)\\)\u3001y\u8ef8\u3068\u306e\u4ea4\u70b9\u306f\\((0,5)\\)\u3067\u3057\u305f\u3002<\/p>\n\n\n\n

      \u3053\u306e2\u70b9\u3092\u6ed1\u3089\u304b\u306b\u3064\u306a\u304e\u3001\u5de6\u53f3\u5bfe\u79f0\u306b\u63cf\u304f\u30682\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u304c\u5b8c\u6210<\/span>\u3057\u307e\u3059\u3002<\/p>\n\n\n

      \n
      \"2\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306e\u66f8\u304d\u65b9\"<\/figure>\n<\/div>\n\n\n

      2\u6b21\u95a2\u6570\u306e\u5f0f\u3092\u30b0\u30e9\u30d5\u306b\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308c\u3070\u3001\u5206\u304b\u3063\u3066\u3044\u308b\u70b9\u304b\u3089\u5143\u3005\u306e\u5f0f\u3092\u6c42\u3081\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n

      2\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u300a\u7df4\u7fd2\u554f\u984c\u300b<\/h2>\n\n\n\n

      2\u6b21\u95a2\u6570\u306e\u66f8\u304d\u65b93\u30b9\u30c6\u30c3\u30d7\u3092\u6d3b\u304b\u3057\u3066\u3001\u4ee5\u4e0b\u306e\u30b0\u30e9\u30d5\u3092\u66f8\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

      \u7df4\u7fd2\u554f\u984c<\/span><\/div>
      \n
        \n
      • \\(y=x^{2}-4x+5\\)<\/li>\n\n\n\n
      • \\(y=-x^{2}+6x-4\\)<\/li>\n\n\n\n
      • \\(y=2x^{2}+8x+5\\)<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n

        \\(y=x^{2}-4x+5\\)\u306e\u30b0\u30e9\u30d5<\/h3>\n\n\n\n

        \u307e\u305a\u5e73\u65b9\u5b8c\u6210\u3057\u3066\u653e\u7269\u7dda\u306e\u8ef8\u3068\u9802\u70b9\u3092\u6c42\u3081\u307e\u3059\u3002<\/p>\n\n\n\n

        \\begin{eqnarray*}
        y&=&x^{2}-4x+5\\\\
        &=&(x-2)^{2}+1
        \\end{eqnarray*}<\/p>\n\n\n\n

        \u3057\u305f\u304b\u3063\u3066\u3001\u9802\u70b9\u306e\u5ea7\u6a19\u306f\\((2,1)\\)\u3068\u5206\u304b\u308a\u307e\u3057\u305f\u3002<\/p>\n\n\n

        \n
        \"\u7df4\u7fd2\u554f\u984c1-1\"<\/figure>\n<\/div>\n\n\n

        \u3064\u304e\u306b\\(y\\)\u8ef8\u3068\u306e\u4ea4\u70b9\u3092\u6c42\u3081\u307e\u3059\u3002<\/p>\n\n\n\n

        \\(x=0\\)\u3092\u4ee3\u5165\u3057\u3066\u3001<\/p>\n\n\n\n

        \\(y=x^{2}-4x+5=0^{2}-4 \\cdot 0 +5=5\\)<\/p>\n\n\n\n

        \u3088\u3063\u3066\u3001\\(y\\)\u8ef8\u3068\u306e\u4ea4\u70b9\u306f\\((0,5)\\)\u3060\u3068\u5206\u304b\u308a\u307e\u3059\u3002<\/p>\n\n\n

        \n
        \"\u7df4\u7fd2\u554f\u984c1-2\"<\/figure>\n<\/div>\n\n\n

        \u653e\u7269\u7dda\u306e\u9802\u70b9\\((2,1)\\)\u3068y\u8ef8\u3068\u306e\u4ea4\u70b9\\((0,5)\\)\u3092\u6ed1\u3089\u304b\u306b\u3064\u306a\u3050\u3068\u5b8c\u6210\u3067\u3059\u3002<\/p>\n\n\n

        \n
        \"\u7df4\u7fd2\u554f\u984c1-3\"<\/figure>\n<\/div>\n\n\n

        \\(y=-x^{2}+6x-4\\)\u306e\u30b0\u30e9\u30d5<\/h3>\n\n\n\n

        \u307e\u305a\u306f\u5e73\u65b9\u5b8c\u6210\u3057\u3066\u8ef8\u3068\u9802\u70b9\u3092\u6c42\u3081\u307e\u3059\u3002<\/p>\n\n\n\n

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

        \u3057\u305f\u304c\u3063\u3066\u3001\u9802\u70b9\u306e\u5ea7\u6a19\u306f\\((3,5)\\)\u3060\u3068\u5206\u304b\u308a\u307e\u3057\u305f\u3002<\/p>\n\n\n

        \n
        \"\u7df4\u7fd2\u554f\u984c2-1\"<\/figure>\n<\/div>\n\n\n

        \u6b21\u306b\\(y\\)\u8ef8\u3068\u306e\u4ea4\u70b9\u3092\u6c42\u3081\u307e\u3059\u3002<\/p>\n\n\n\n

        \\(x=0\\)\u3092\u4ee3\u5165\u3057\u3066\u3001<\/p>\n\n\n\n

        \\(y=-x^{2}+6x-4=0^{2}+6 \\cdot 0 -4=-4\\)<\/p>\n\n\n\n

        \u3088\u3063\u3066\u3001\\(y\\)\u8ef8\u3068\u306e\u4ea4\u70b9\u306f\\((0,-4)\\)\u3060\u3068\u5206\u304b\u308a\u307e\u3059\u3002<\/p>\n\n\n

        \n
        \"\u7df4\u7fd2\u554f\u984c2-2\"<\/figure>\n<\/div>\n\n\n

        \u653e\u7269\u7dda\u306e\u9802\u70b9\\((3,5)\\)\u3068y\u8ef8\u3068\u306e\u4ea4\u70b9\\((0,-4)\\)\u3092\u6ed1\u3089\u304b\u306b\u3064\u306a\u3050\u3068\u5b8c\u6210\u3067\u3059\u3002<\/p>\n\n\n

        \n
        \"\u7df4\u7fd2\u554f\u984c2-3\"<\/figure>\n<\/div>\n\n\n

        \\(y=2x^{2}+8x+5\\)\u306e\u30b0\u30e9\u30d5<\/h3>\n\n\n\n

        \u307e\u305a\u306f\u5e73\u65b9\u5b8c\u6210\u3057\u3066\u8ef8\u3068\u9802\u70b9\u3092\u6c42\u3081\u307e\u3059\u3002<\/p>\n\n\n\n

        \\begin{eqnarray}
        y&=&2x^{2}+8x+5\\\\
        &=&2(x^{2}+4x)+5\\\\
        &=&2\\{(x+2)^{2}-4\\}+5\\\\
        &=&2(x+2)^{2}-3\\\\
        \\end{eqnarray}<\/p>\n\n\n\n

        \u3057\u305f\u304c\u3063\u3066\u3001\u9802\u70b9\u306e\u5ea7\u6a19\u306f\\((-2,-3)\\)\u3060\u3068\u5206\u304b\u308a\u307e\u3057\u305f\u3002<\/p>\n\n\n

        \n
        \"\u7df4\u7fd2\u554f\u984c3-1\"<\/figure>\n<\/div>\n\n\n

        \u6b21\u306b\\(y\\)\u8ef8\u3068\u306e\u4ea4\u70b9\u3092\u6c42\u3081\u307e\u3059\u3002<\/p>\n\n\n\n

        \\(x=0\\)\u3092\u4ee3\u5165\u3057\u3066\u3001<\/p>\n\n\n\n

        \\(y=2x^{2}+8x+5=2 \\cdot 0^{2}+8 \\cdot 0 +5=5\\)<\/p>\n\n\n\n

        \u3088\u3063\u3066\u3001\\(y\\)\u8ef8\u3068\u306e\u4ea4\u70b9\u306f\\((0,5)\\)\u3060\u3068\u5206\u304b\u308a\u307e\u3059\u3002<\/p>\n\n\n

        \n
        \"\u7df4\u7fd2\u554f\u984c3-2\"<\/figure>\n<\/div>\n\n\n

        \u653e\u7269\u7dda\u306e\u9802\u70b9\\((-2,-3)\\)\u3068y\u8ef8\u3068\u306e\u4ea4\u70b9\\((0,5)\\)\u3092\u6ed1\u3089\u304b\u306b\u3064\u306a\u3050\u3068\u5b8c\u6210\u3067\u3059\u3002<\/p>\n\n\n

        \n
        \"\u7df4\u7fd2\u554f\u984c3-3\"<\/figure>\n<\/div>\n\n\n

        2\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u3000\u307e\u3068\u3081<\/h2>\n\n\n\n

        \u4eca\u56de\u306f2\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306e\u66f8\u304d\u65b9\u306b\u3064\u3044\u3066\u307e\u3068\u3081\u307e\u3057\u305f\u3002<\/span><\/p>\n\n\n\n

        \n

        2\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306e\u5f62<\/p>\n\n\n\n

        \\(a>0\\)\u306e\u3068\u304d\u3001\u4e0b\u5411\u304d\u306b\u51f8\u306a\u653e\u7269\u7dda
        \\(a<0\\)\u306e\u3068\u304d\u3001\u4e0a\u5411\u304d\u306b\u51f8\u306a\u653e\u7269\u7dda<\/p>\n<\/div><\/div>\n\n\n\n

        \n

        2\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306e\u5f62<\/p>\n\n\n\n

        \\(a>0\\)\u306e\u3068\u304d\u3001\u4e0b\u5411\u304d\u306b\u51f8\u306a\u653e\u7269\u7dda
        \\(a<0\\)\u306e\u3068\u304d\u3001\u4e0a\u5411\u304d\u306b\u51f8\u306a\u653e\u7269\u7dda<\/p>\n<\/div><\/div>\n\n\n\n

        \n

        \u30b0\u30e9\u30d5\u3092\u66f8\u304f\u624b\u9806<\/p>\n\n\n\n

        1.\u8ef8\u3068\u9802\u70b9\u3092\u6c42\u3081\u308b
        2.y\u8ef8\u3068\u306e\u4ea4\u70b9\u3092\u6c42\u3081\u308b
        3.\u9802\u70b9\u3068y\u8ef8\u3068\u306e\u4ea4\u70b9\u3092\u6ed1\u3089\u304b\u306b\u3064\u306a\u3050<\/p>\n<\/div><\/div>\n\n\n\n

        2\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u304c\u66f8\u3051\u306a\u3044\u3068\u3001\u6700\u5927\u5024\u30fb\u6700\u5c0f\u5024\u3092\u6c42\u3081\u308b\u554f\u984c\u3067\u304b\u306a\u308a\u82e6\u6226\u3057\u307e\u3059\u3002<\/span><\/p>\n\n\n\n

        \u6c7a\u3057\u3066\u96e3\u3057\u3044\u624b\u9806\u3067\u306f\u306a\u3044\u306e\u3067\u3001\u5fc5\u305a\u30b0\u30e9\u30d5\u3092\u66f8\u3051\u308b\u3088\u3046\u306b\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

        \u305d\u308c\u3067\u306f\u6700\u5f8c\u307e\u3067\u3054\u89a7\u3044\u305f\u3060\u304d\u3042\u308a\u304c\u3068\u3046\u3054\u3056\u3044\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

        \u307f\u3093\u306a\u306e\u52aa\u529b\u304c\u5831\u308f\u308c\u307e\u3059\u3088\u3046\u306b\uff01<\/p>\n","protected":false},"excerpt":{"rendered":"

        \u6570\u5b66\u2160\u306e\u4e8c\u6b21\u95a2\u6570\u3067\u306f\u30b0\u30e9\u30d5\u304c\u5fc5\u8981\u306a\u554f\u984c\u304c\u305f\u304f\u3055\u3093\u3042\u308a\u307e\u3059\u3002 \u4eca\u56de\u306f2\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306b\u95a2\u3059\u308b\u3053\u3093\u306a\u60a9\u307f\u3092\u89e3\u6c7a\u3057\u307e\u3059\u3002 2\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306f\u4ee5\u4e0b\u306e3\u30b9\u30c6\u30c3\u30d7\u3067\u66f8\u304f\u3068\u4e0a\u624b\u306b\u63cf\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 \u672c\u8a18\u4e8b\u3067\u306f2\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306e\u66f8\u304d\u65b9 […]<\/p>\n","protected":false},"author":1,"featured_media":5457,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"swell_btn_cv_data":"","footnotes":""},"categories":[21,222],"tags":[22,10,11],"class_list":["post-5451","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-nizikansuu","category-math-1","tag-22","tag-a","tag-11"],"yoast_head":"\n\u4e8c\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306e\u66f8\u304d\u65b9\u30103\u30b9\u30c6\u30c3\u30d7\u3011\u3067\u8ab0\u3067\u3082\u8ff7\u308f\u305a\u66f8\u3051\u308b\u624b\u9806\u3092\u516c\u958b<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/math-travel.jp\/math-1\/quadratic-graph\/\" \/>\n<meta property=\"og:locale\" content=\"ja_JP\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u4e8c\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306e\u66f8\u304d\u65b9\u30103\u30b9\u30c6\u30c3\u30d7\u3011\u3067\u8ab0\u3067\u3082\u8ff7\u308f\u305a\u66f8\u3051\u308b\u624b\u9806\u3092\u516c\u958b\" \/>\n<meta property=\"og:description\" content=\"\u6570\u5b66\u2160\u306e\u4e8c\u6b21\u95a2\u6570\u3067\u306f\u30b0\u30e9\u30d5\u304c\u5fc5\u8981\u306a\u554f\u984c\u304c\u305f\u304f\u3055\u3093\u3042\u308a\u307e\u3059\u3002 \u4eca\u56de\u306f2\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306b\u95a2\u3059\u308b\u3053\u3093\u306a\u60a9\u307f\u3092\u89e3\u6c7a\u3057\u307e\u3059\u3002 2\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306f\u4ee5\u4e0b\u306e3\u30b9\u30c6\u30c3\u30d7\u3067\u66f8\u304f\u3068\u4e0a\u624b\u306b\u63cf\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 \u672c\u8a18\u4e8b\u3067\u306f2\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306e\u66f8\u304d\u65b9 […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/math-travel.jp\/math-1\/quadratic-graph\/\" \/>\n<meta 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