{"id":5491,"date":"2025-12-24T17:18:16","date_gmt":"2025-12-24T08:18:16","guid":{"rendered":"https:\/\/math-travel.com\/?p=5491"},"modified":"2026-02-11T16:24:26","modified_gmt":"2026-02-11T07:24:26","slug":"tyouten-ziku","status":"publish","type":"post","link":"https:\/\/math-travel.jp\/math-1\/tyouten-ziku\/","title":{"rendered":"\u4e8c\u6b21\u95a2\u6570\u306e\u9802\u70b9\u30fb\u8ef8\u306e\u6c42\u3081\u65b9\u30fc\u5e73\u65b9\u5b8c\u6210\u306e\u30b3\u30c4\u3092\u63b4\u3093\u3067\u8a08\u7b97\u30df\u30b9\u3092\u9632\u3050\u65b9\u6cd5"},"content":{"rendered":"\n<p>\u6570\u5b66\u2160\u4e8c\u6b21\u95a2\u6570\u306b\u306f<span class=\"huto\">\u300c\u8ef8\u3068\u9802\u70b9\u3092\u6c42\u3081\u308b\u554f\u984c\u300d<\/span>\u304c\u591a\u304f\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u672c\u8a18\u4e8b\u3067\u306f\u30012\u6b21\u95a2\u6570\u306e\u9802\u70b9\u3084\u8ef8\u306e\u6c42\u3081\u65b9\u3092\u89e3\u8aac\u3057\u307e\u3059\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" width=\"351\" height=\"205\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2021\/05\/\u4e8c\u6b21\u95a2\u6570\u306e\u8ef8\u3068\u9802\u70b91.png\" alt=\"\u4e8c\u6b21\u95a2\u6570 \u9802\u70b9 \u8ef8\" class=\"wp-image-5500\" srcset=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2021\/05\/\u4e8c\u6b21\u95a2\u6570\u306e\u8ef8\u3068\u9802\u70b91.png 351w, https:\/\/math-travel.jp\/wp-content\/uploads\/2021\/05\/\u4e8c\u6b21\u95a2\u6570\u306e\u8ef8\u3068\u9802\u70b91-300x175.png 300w\" sizes=\"(max-width: 351px) 100vw, 351px\" \/><\/figure>\n<\/div>\n\n\n<p><br>\n2\u6b21\u95a2\u6570\u306e\u8ef8\u3084\u9802\u70b9\u306f\u4ee5\u4e0b\u306e\u5f62\u3067\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<div class=\"swell-block-capbox cap_box\"><div class=\"cap_box_ttl\"><span>2\u6b21\u95a2\u6570\u306e\u8ef8\u30fb\u9802\u70b9<\/span><\/div><div class=\"cap_box_content\">\n<p>2\u6b21\u95a2\u6570\\(y=a(x-p)^{2}+q\\)\u306b\u304a\u3044\u3066\u3001<\/p>\n\n\n\n<p>\u653e\u7269\u7dda\u306e\u8ef8\uff1a\\(x=p\\)<br>\u9802\u70b9\u306e\u5ea7\u6a19\uff1a\\((p,q)\\)<\/p>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"tyouten\">2\u6b21\u95a2\u6570\u306e\u8ef8\u3068\u9802\u70b9<\/h2>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" width=\"351\" height=\"205\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2021\/05\/\u4e8c\u6b21\u95a2\u6570\u306e\u8ef8\u3068\u9802\u70b91.png\" alt=\"\u4e8c\u6b21\u95a2\u6570 \u9802\u70b9 \u8ef8\" class=\"wp-image-5500\" srcset=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2021\/05\/\u4e8c\u6b21\u95a2\u6570\u306e\u8ef8\u3068\u9802\u70b91.png 351w, https:\/\/math-travel.jp\/wp-content\/uploads\/2021\/05\/\u4e8c\u6b21\u95a2\u6570\u306e\u8ef8\u3068\u9802\u70b91-300x175.png 300w\" sizes=\"(max-width: 351px) 100vw, 351px\" \/><\/figure>\n<\/div>\n\n\n<div class=\"swell-block-capbox cap_box\"><div class=\"cap_box_ttl\"><span><span class=\"huto\">2\u6b21\u95a2\u6570\u306e\u8ef8\u30fb\u9802\u70b9<\/span><\/span><\/div><div class=\"cap_box_content\">\n<p>2\u6b21\u95a2\u6570 \\(y=a(x-p)^{2}+q\\)\u306b\u304a\u3044\u3066\u3001<\/p>\n\n\n\n<p>\u653e\u7269\u7dda\u306e\u8ef8\uff1a\\(x=p\\)<br>\u9802\u70b9\u306e\u5ea7\u6a19\uff1a\\((p,q)\\)<\/p>\n<\/div><\/div>\n\n\n\n<p>2\u6b21\u95a2\u6570\u306e\u8ef8\u3084\u9802\u70b9\u3092\u6c42\u3081\u308b\u306b\u306f\u3001\u5f0f\u3092\u4ee5\u4e0b\u306e\u5f62\u306b\u3059\u308b\u3053\u3068\u3067\u6c42\u3081\u3089\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p>\\[y=a(x-p)^{2}+q\\]<\/p>\n\n\n\n<p>\u3053\u306e2\u6b21\u95a2\u6570\u306f\\(y=ax^{2}\\)\u306e\u30b0\u30e9\u30d5\u3092x\u8ef8\u65b9\u5411\u306b\\(p\\)\u3001y\u8ef8\u65b9\u5411\u306b\\(q\\)\u3060\u3051\u5e73\u884c\u79fb\u52d5\u3057\u305f2\u6b21\u95a2\u6570\u3092\u8868\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n<div class=\"swell-block-balloon\"><div class=\"c-balloon -bln-left\" data-col=\"gray\"><div class=\"c-balloon__icon -circle\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2024\/05\/math-travel-hukidashi8-150x150.webp\" alt=\"\" class=\"c-balloon__iconImg\" width=\"80px\" height=\"80px\"><span class=\"c-balloon__iconName\">\u9ad8\u6821\u751f<\/span><\/div><div class=\"c-balloon__body -speaking -border-on\"><div class=\"c-balloon__text\">\n<p>\u3060\u304b\u3089\u9802\u70b9\u304c\\((p,q)\\)\u306b\u306a\u308b\u3093\u3067\u3059\u306d\uff01<\/p>\n<span class=\"c-balloon__shapes\"><span class=\"c-balloon__before\"><\/span><span class=\"c-balloon__after\"><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"motomekata\">\u9802\u70b9\u3068\u8ef8\u306e\u6c42\u3081\u65b9<\/h2>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" width=\"351\" height=\"205\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2021\/05\/\u4e8c\u6b21\u95a2\u6570\u306e\u8ef8\u3068\u9802\u70b91.png\" alt=\"\u4e8c\u6b21\u95a2\u6570 \u9802\u70b9 \u8ef8 \u6c42\u3081\u65b9\" class=\"wp-image-5500\" srcset=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2021\/05\/\u4e8c\u6b21\u95a2\u6570\u306e\u8ef8\u3068\u9802\u70b91.png 351w, https:\/\/math-travel.jp\/wp-content\/uploads\/2021\/05\/\u4e8c\u6b21\u95a2\u6570\u306e\u8ef8\u3068\u9802\u70b91-300x175.png 300w\" sizes=\"(max-width: 351px) 100vw, 351px\" \/><\/figure>\n<\/div>\n\n\n<p><span class=\"huto\">2\u6b21\u95a2\u6570\u306e\u9802\u70b9\u3068\u8ef8\u306e\u6c42\u3081\u65b9<\/span>\u306f\u4e3b\u306b2\u3064\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<div class=\"swell-block-capbox cap_box\"><div class=\"cap_box_ttl\"><span><span class=\"huto\">\u8ef8\u30fb\u9802\u70b9\u306e\u6c42\u3081\u65b9<\/span><\/span><\/div><div class=\"cap_box_content\">\n<ol class=\"wp-block-list\">\n<li>\u5e73\u65b9\u5b8c\u6210\u3057\u3066\u6c42\u3081\u308b\u65b9\u6cd5<\/li>\n\n\n\n<li>\u516c\u5f0f\u306b\u4ee3\u5165\u3057\u3066\u6c42\u3081\u308b\u65b9\u6cd5<\/li>\n<\/ol>\n<\/div><\/div>\n\n\n<div class=\"swell-block-balloon\"><div class=\"c-balloon -bln-right\" data-col=\"gray\"><div class=\"c-balloon__icon -circle\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2024\/05\/math-travel-hukidashi1-150x150.webp\" alt=\"\" class=\"c-balloon__iconImg\" width=\"80px\" height=\"80px\"><span class=\"c-balloon__iconName\">\u30b7\u30fc\u30bf<\/span><\/div><div class=\"c-balloon__body -speaking -border-on\"><div class=\"c-balloon__text\">\n<p>\u5e73\u65b9\u5b8c\u6210\u3067\u6c42\u3081\u308b\u306e\u304c\u4e00\u822c\u7684\u3067\u3059\uff01<\/p>\n<span class=\"c-balloon__shapes\"><span class=\"c-balloon__before\"><\/span><span class=\"c-balloon__after\"><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n<h3 class=\"wp-block-heading\">\u5e73\u65b9\u5b8c\u6210\u3067\u6c42\u3081\u308b\u65b9\u6cd5<\/h3>\n\n\n\n<p><span class=\"huto\">\u307e\u305a\u306f\u5e73\u65b9\u5b8c\u6210\u3092\u7528\u3044\u3066\u8ef8\u3068\u9802\u70b9\u3092\u6c42\u3081\u308b\u65b9\u6cd5\u304b\u3089\u89e3\u8aac\u3057\u307e\u3059\u3002<\/span><\/p>\n\n\n\n<p>\u5e73\u65b9\u5b8c\u6210\u3068\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u5f0f\u5909\u5f62\u3067\u3059\u3002<\/p>\n\n\n\n<p>\\begin{eqnarray}<br>x^{2}+4x&amp;=&amp;(x^{2}+4x+4)-4\\<br>&amp;=&amp;(x+2)^{2}-4<br>\\end{eqnarray}<\/p>\n\n\n\n<p>\\begin{eqnarray}<br>x^{2}-6x+4&amp;=&amp;(x^{2}-6x+9)-9+4\\<br>&amp;=&amp;(x-3)^{2}-5<br>\\end{eqnarray}<\/p>\n\n\n\n<p>2\u6b21\u95a2\u6570\\(x^{2}+6x+5\\)\u306e\u30b0\u30e9\u30d5\u306e\u8ef8\u3068\u9802\u70b9\u3092\u6c42\u3081\u307e\u3059\u3002<\/p>\n\n\n\n<p>\\begin{eqnarray}<br>\nx^{2}+6x+5&amp;=&amp;(x^{2}+6x+9)-9+5\\\\<br>\n&amp;=&amp;(x+3)^{2}-4<br>\n\\end{eqnarray}<\/p>\n\n\n\n<p>\u3053\u3053\u3067\u4ee5\u4e0b\u306e\u3053\u3068\u3092\u601d\u3044\u51fa\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n<div class=\"wp-block-group has-border -border01\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p>2\u6b21\u95a2\u6570(y=a(x-p)^{2}+q)\u306e\u3068\u304d\u3001<\/p>\n\n\n\n<p>\u653e\u7269\u7dda\u306e\u8ef8\uff1a(x=p)<br>\u9802\u70b9\u306e\u5ea7\u6a19\uff1a((p,q))<\/p>\n<\/div><\/div>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" width=\"939\" height=\"524\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2021\/05\/\u4e8c\u6b21\u95a2\u6570\u306e\u8ef8\u3068\u9802\u70b92.png\" alt=\"\u5e73\u65b9\u5b8c\u6210\u3067\u6c42\u3081\u308b\u65b9\u6cd5\" class=\"wp-image-7558\" srcset=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2021\/05\/\u4e8c\u6b21\u95a2\u6570\u306e\u8ef8\u3068\u9802\u70b92.png 939w, https:\/\/math-travel.jp\/wp-content\/uploads\/2021\/05\/\u4e8c\u6b21\u95a2\u6570\u306e\u8ef8\u3068\u9802\u70b92-300x167.png 300w, https:\/\/math-travel.jp\/wp-content\/uploads\/2021\/05\/\u4e8c\u6b21\u95a2\u6570\u306e\u8ef8\u3068\u9802\u70b92-768x429.png 768w\" sizes=\"(max-width: 939px) 100vw, 939px\" \/><\/figure>\n<\/div>\n\n\n<p>\\((x+3)^{2}-4\\)\u306e\u30b0\u30e9\u30d5\u306e\u8ef8\u3068\u9802\u70b9\u306f\u3001<\/p>\n\n\n\n<p>\u653e\u7269\u7dda\u306e\u8ef8\uff1a\\(x=-3\\)<br>\n\u9802\u70b9\u306e\u5ea7\u6a19\uff1a\\((-3,-4)\\)<\/p>\n\n\n\n<p>\u3060\u3068\u5206\u304b\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3053\u308c\u3067\\(y=x^{2}+6x+5\\)\u306e\u8ef8\u3068\u9802\u70b9\u306e\u5ea7\u6a19\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<p>\u3053\u306e\u3088\u3046\u306b\u3001\u5e73\u65b9\u5b8c\u6210\u3092\u3057\u3066\\(y=a(x-p)^{2}+q\\)\u306e\u5f62\u306b\u3067\u304d\u308c\u3070\u3001\u8ef8\u3082\u9802\u70b9\u304c\u5206\u304b\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u516c\u5f0f\u3092\u6697\u8a18\u3057\u3066\u6c42\u3081\u308b\u65b9\u6cd5<\/h3>\n\n\n\n<p>\uff12\u6b21\u95a2\u6570\u306e\u8ef8\u3068\u9802\u70b9\u3092\u6c42\u3081\u308b\u3082\u30461\u3064\u306e\u65b9\u6cd5\u3068\u3057\u3066\u3001<span class=\"huto\">\u516c\u5f0f\u306b\u4ee3\u5165\u3059\u308b\u65b9\u6cd5<\/span>\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u305f\u3060\u3057\u3053\u306e\u3084\u308a\u65b9\u306f\u3001<span class=\"hutoaka\">\u4ee5\u4e0b\u306e\u516c\u5f0f\u3092\u899a\u3048\u308b\u5fc5\u8981\u304c\u3042\u308b\u306e\u3067\u3042\u307e\u308a\u30aa\u30b9\u30b9\u30e1\u306f\u3057\u307e\u305b\u3093\u3002<\/span><\/p>\n\n\n\n<div class=\"swell-block-capbox cap_box\"><div class=\"cap_box_ttl\"><span>\u8ef8\u3068\u9802\u70b9\u306e\u516c\u5f0f<\/span><\/div><div class=\"cap_box_content\">\n<p>\\(y=ax^{2}+bx+c\\)\u306e\u30b0\u30e9\u30d5\u306b\u304a\u3044\u3066<\/p>\n\n\n\n<p>\u653e\u7269\u7dda\u306e\u8ef8\uff1a\\(\\displaystyle x=-\\frac{b}{2a}\\)<\/p>\n\n\n\n<p>\u9802\u70b9\u306e\u5ea7\u6a19\uff1a\\(\\displaystyle (-\\frac{b}{2a},-\\frac{b^{2}-4ac}{4a})\\)<\/p>\n<\/div><\/div>\n\n\n\n<p>2\u6b21\u95a2\u6570\\(x^{2}+6x+5\\)\u306e\u3068\u304d\u306e\u8ef8\u306f<\/p>\n\n\n\n<p>\\begin{eqnarray}<br>\nx&amp;=&amp;-\\frac{b}{2a}\\\\<br>\n&amp;=&amp;-\\frac{6}{2 \\cdot 1}\\\\<br>\n&amp;=&amp;-3<br>\n\\end{eqnarray}<\/p>\n\n\n\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u653e\u7269\u7dda\u306e\u8ef8\u306f\\(x=-3\\)<\/p>\n\n\n\n<p>&nbsp;<\/p>\n\n\n\n<p>\u307e\u305f\u30012\u6b21\u95a2\u6570\\(x^{2}+6x+5\\)\u306e\u9802\u70b9\u306f<\/p>\n\n\n\n<p>\\begin{eqnarray}<br>\n\u9802\u70b9\u306ey\u5ea7\u6a19&amp;=&amp;-\\frac{b^{2}-4ac}{4a}\\\\<br>\n&amp;=&amp;-\\frac{6^{2}-4 \\cdot 1 \\cdot 5}{4 \\cdot 1}\\\\<br>\n&amp;=&amp;-4<br>\n\\end{eqnarray}<\/p>\n\n\n\n<p>\u3057\u305f\u304c\u3063\u3066\u30012\u6b21\u95a2\u6570\\(x^{2}+6x+5\\)\u306e\u9802\u70b9\u306f\\((-3,-4)\\)\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n<div class=\"swell-block-balloon\"><div class=\"c-balloon -bln-right\" data-col=\"gray\"><div class=\"c-balloon__icon -circle\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2024\/05\/math-travel-hukidashi1-150x150.webp\" alt=\"\" class=\"c-balloon__iconImg\" width=\"80px\" height=\"80px\"><span class=\"c-balloon__iconName\">\u30b7\u30fc\u30bf<\/span><\/div><div class=\"c-balloon__body -speaking -border-on\"><div class=\"c-balloon__text\">\n<p>\u516c\u5f0f\u3092\u899a\u3048\u308b\u306e\u306f\u5927\u5909\u306a\u306e\u3067\u3001\u5e73\u65b9\u5b8c\u6210\u306e\u65b9\u6cd5\u304c\u304a\u3059\u3059\u3081\u3060\u3088\u3002<\/p>\n<span class=\"c-balloon__shapes\"><span class=\"c-balloon__before\"><\/span><span class=\"c-balloon__after\"><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n<p>\u5e73\u65b9\u5b8c\u6210\u304c\u3067\u304d\u308c\u30702\u6b21\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u3092\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<div class=\"wp-block-group is-style-bg_stripe\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p><span class=\"huto\">2\u6b21\u95a2\u6570\u306e\u81ea\u52d5\u8a08\u7b97\u5668<\/span><\/p>\n\n\n\n<div id=\"kv\">\n        <p>\u4e8c\u6b21\u95a2\u6570\u306e\u9802\u70b9\u3092\u7b97\u51fa\u3057\u307e\u3059\u3002a,b,c\u306b\u5024\u3092\u5165\u529b\u3057\u3066\u3001\u300c\u7b97\u51fa\u300d\u30dc\u30bf\u30f3\u3092\u62bc\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n      <\/div>\n      <div id=\"input\">\n        <p>\\(y=ax^{2}+bx+c\\)<\/p>\n        <div>\n          <div class=\"input-number\">\n            <label for=\"a1\">a:<\/label>\n            <input type=\"number\" name=\"a1\" id=\"a1\">\n          <\/div>\n          <div class=\"input-number\">\n            <label for=\"a2\">b:<\/label>\n            <input type=\"number\" name=\"a2\" id=\"a2\">\n          <\/div>\n          <div class=\"input-number\">\n            <label for=\"a3\">c:<\/label>\n            <input type=\"number\" name=\"a3\" id=\"a3\">\n          <\/div>\n        <\/div>\n      <\/div>\n      <div id=\"output\">\n        <p>\u4e8c\u6b21\u95a2\u6570 <span id=\"input-formula\"><\/span> \u306f <span id=\"output-formula\"><\/span> \u3068\u66f8\u304d\u63db\u3048\u308b\u3053\u3068\u304c\u53ef\u80fd\u306a\u306e\u3067\u3001<\/p>\n        <div class=\"output-number\">\n          <p>\u9802\u70b9\u306e\u5ea7\u6a19\u306f(<span class=\"p-number\"><\/span>,<span class=\"q-number\"><\/span>)\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n        <\/div>\n      <\/div>\n      <div id=\"output-error\">\n        <p id=\"error-text\"><\/p>\n      <\/div>\n      <div id=\"btn\">\n        <input type=\"button\" value=\"\u7b97\u51fa\" id=\"calBtn\">\n        <input type=\"button\" value=\"\u30ea\u30bb\u30c3\u30c8\" id=\"reset-btn\">\n      <\/div>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"bunsuu\">\u5206\u6570\u3084\u30de\u30a4\u30ca\u30b9\u3092\u3082\u30642\u6b21\u95a2\u6570\u306e\u9802\u70b9<\/h2>\n\n\n\n<p>\u4ee5\u4e0b\u306e2\u3064\u306e\u5f0f\u306e\u3088\u3046\u306b\u3001\u9802\u70b9\u3092\u6c42\u3081\u305f\u30442\u6b21\u95a2\u6570\u304c\u5206\u6570\u30fb\u30de\u30a4\u30ca\u30b9\u3092\u542b\u3080\u5834\u5408\u3082\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\\[\\displaystyle y=x^{2}+\\frac{6}{5}x+3 \\cdots \u2460\\]<\/p>\n\n\n\n<p>\\[y=-x^{2}+6x+3 \\cdots \u2461\\]<\/p>\n\n\n\n<p>\u96e3\u3057\u305d\u3046\u306b\u898b\u3048\u307e\u3059\u304c\u3001\u843d\u3061\u7740\u3044\u3066\u5bfe\u51e6\u3059\u308c\u3070\u554f\u984c\u306a\u3044\u3067\u3059\u3002<\/p>\n\n\n<div class=\"swell-block-balloon\"><div class=\"c-balloon -bln-right\" data-col=\"gray\"><div class=\"c-balloon__icon -circle\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2024\/05\/math-travel-hukidashi4-150x150.webp\" alt=\"\" class=\"c-balloon__iconImg\" width=\"80px\" height=\"80px\"><span class=\"c-balloon__iconName\">\u30b7\u30fc\u30bf<\/span><\/div><div class=\"c-balloon__body -speaking -border-on\"><div class=\"c-balloon__text\">\n<p>\u5f0f\u306b\u5206\u6570\u304c\u3042\u308b\u3060\u3051\u3067\u5acc\u306a\u611f\u3058\u304c\u3057\u307e\u3059\u3088\u306d\u2026\u3002<\/p>\n<span class=\"c-balloon__shapes\"><span class=\"c-balloon__before\"><\/span><span class=\"c-balloon__after\"><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n<h3 class=\"wp-block-heading\">\u5206\u6570\u3092\u542b\u30802\u6b21\u95a2\u6570<\/h3>\n\n\n\n<p>2\u6b21\u95a2\u6570\\(\\displaystyle x^{2}+\\frac{6}{5}x+3\\)\u306e\u8ef8\u3068\u9802\u70b9\u3092\u8003\u3048\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n<p>\u3084\u306f\u308a\u6c17\u306b\u306a\u308b\u306e\u306f\u3001<span class=\"hutoaka\">\\(\\displaystyle \\frac{6}{5}x\\)<\/span>\u3067\u3059\u3088\u306d\u3002<\/p>\n\n\n\n<p>&nbsp;\u4eca\u56de\u306f\u5e73\u65b9\u5b8c\u6210\u3092\u7528\u3044\u305f\u6c42\u3081\u65b9\u3092\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\\begin{eqnarray}<br>\ny&amp;=&amp;x^{2}+\\frac{6}{5}x+3\\\\<br>\n&amp;=&amp;(x^{2}+\\frac{6}{5}x+\\frac{9}{25})-\\frac{9}{25}+3\\\\<br>\n&amp;=&amp;(x+\\frac{3}{5})^{2}+\\frac{66}{25}\\\\<br>\n\\end{eqnarray}<\/p>\n\n\n\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u5206\u6570\u3092\u542b\u30802\u6b21\u95a2\u6570\u306e\u8ef8\u30fb\u9802\u70b9\u3082\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<p>\u653e\u7269\u7dda\u306e\u8ef8\uff1a\\(\\displaystyle x=-\\frac{3}{5}\\)<br>\n\u9802\u70b9\u306e\u5ea7\u6a19\uff1a\\(\\displaystyle (-\\frac{3}{5},\\frac{66}{25})\\)<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u30de\u30a4\u30ca\u30b9\u3092\u542b\u30802\u6b21\u95a2\u6570<\/h3>\n\n\n\n<p>\u6b21\u306b\u30de\u30a4\u30ca\u30b9\u3092\u542b\u30802\u6b21\u95a2\u6570\u3082\u307f\u3066\u3044\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n<p>\\(-x^{2}+6x+3\\)\u306e\u8ef8\u3068\u9802\u70b9\u306e\u5ea7\u6a19\u3092\u6c42\u3081\u307e\u3059\u3002<\/p>\n\n\n\n<p>\\begin{eqnarray}<br>\ny&amp;=&amp;-x^{2}+6x+3\\\\<br>\n&amp;=&amp;-(x^{2}-6x)+3\\\\<br>\n&amp;=&amp;-{(x^{2}-6x+9)-9}+3\\\\<br>\n&amp;=&amp;-(x-3)^{2}+12\\\\<br>\n\\end{eqnarray}<\/p>\n\n\n\n<p>\u3057\u305f\u304c\u3063\u3066\u3001<\/p>\n\n\n\n<p>\u653e\u7269\u7dda\u306e\u8ef8\uff1a\\(x=3\\)<br>\n\u9802\u70b9\u306e\u5ea7\u6a19\uff1a\\(\\displaystyle (3,12)\\)<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"osusume\">\u9802\u70b9\u3068\u8ef8\u306e\u6c42\u3081\u65b9\u300a\u304a\u3059\u3059\u3081\u52d5\u753b\u300b<\/h2>\n\n\n\n<p>\u3053\u3053\u307e\u3067\u8ef8\u3068\u9802\u70b9\u306e\u6c42\u3081\u65b9\u3092\u89e3\u8aac\u3057\u3066\u304d\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<p><span class=\"hutoaka\">\u300c\u30a4\u30de\u30a4\u30c1\u5206\u304b\u3089\u306a\u3044\u306a\u3041&#8230;\u300d<\/span><\/p>\n\n\n\n<p>\u305d\u3093\u306a\u65b9\u306f\u4e0b\u306e\u52d5\u753b\u304c\u304a\u3059\u3059\u3081\u3067\u3059\u3002<\/p>\n\n\n\n<p>\u25bd2\u6b21\u95a2\u6570\u306e\u8ef8\u3068\u9802\u70b9\u306e\u8aac\u660e\u3092\u3057\u3066\u3044\u307e\u3059<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"\u3010\u9ad8\u6821\u6570\u5b66\u3011\u6570\u2160-37 \uff12\u6b21\u95a2\u6570\u2462(\u8ef8\u3068\u9802\u70b9\u7de8)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/sxlmZoowMOU?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"mondai\">\u9802\u70b9\u3068\u8ef8\u306e\u6c42\u3081\u65b9\u300a\u7df4\u7fd2\u554f\u984c\u300b<\/h2>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" width=\"500\" height=\"365\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2021\/06\/Mathematics-cuate-e1633999100291.png\" alt=\"\u9802\u70b9\u3068\u8ef8\u306e\u6c42\u3081\u65b9\u300a\u7df4\u7fd2\u554f\u984c\u300b\" class=\"wp-image-7269\" srcset=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2021\/06\/Mathematics-cuate-e1633999100291.png 500w, https:\/\/math-travel.jp\/wp-content\/uploads\/2021\/06\/Mathematics-cuate-e1633999100291-300x219.png 300w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><\/figure>\n<\/div>\n\n\n<p>\u305d\u308c\u3067\u306f\u30012\u6b21\u95a2\u6570\u306e\u8ef8\u3068\u9802\u70b9\u3092\u6c42\u3081\u308b\u7df4\u7fd2\u3092\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n<p>\u4ee5\u4e0b\u306e2\u6b21\u95a2\u6570\u306e\u8ef8\u3068\u9802\u70b9\u3092\u6c42\u3081\u307e\u3059\u3002<\/p>\n\n\n\n<div class=\"swell-block-capbox cap_box\"><div class=\"cap_box_ttl\"><span><span class=\"huto\">\u7df4\u7fd2\u554f\u984c<\/span><\/span><\/div><div class=\"cap_box_content\">\n<ul class=\"wp-block-list\">\n<li>\\(y=x^{2}+2x+4\\)<\/li>\n\n\n\n<li>\\(y=3x^{2}+6x-4\\)<\/li>\n\n\n\n<li>\\(y=-2x^{2}-4x+5\\)<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">\\(y=x^{2}+2x+4\\)\u306e\u8ef8\u3068\u9802\u70b9<\/h3>\n\n\n\n<p>2\u6b21\u95a2\u6570\\(y=x^{2}+2x+4\\)\u3092\u5e73\u65b9\u5b8c\u6210\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\\begin{eqnarray}<br>\ny&amp;=&amp;x^{2}+2x+4\\\\<br>\n&amp;=&amp;(x^{2}+2x+1)-1+4\\\\<br>\n&amp;=&amp;(x+1)^{2}+3<br>\n\\end{eqnarray}<\/p>\n\n\n\n<p>\u3057\u305f\u304c\u3063\u3066\u3001<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" width=\"623\" height=\"404\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2021\/05\/\u7df4\u7fd2\u554f\u984c1.png\" alt=\"\u9802\u70b9\u3068\u8ef8\u306e\u6c42\u3081\u65b9\u300a\u7df4\u7fd2\u554f\u984c\u300b\" class=\"wp-image-7559\" srcset=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2021\/05\/\u7df4\u7fd2\u554f\u984c1.png 623w, https:\/\/math-travel.jp\/wp-content\/uploads\/2021\/05\/\u7df4\u7fd2\u554f\u984c1-300x195.png 300w\" sizes=\"(max-width: 623px) 100vw, 623px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-border -border01\">\u89e3\u7b54<br> \u653e\u7269\u7dda\u306e\u8ef8\uff1a\\(x=-1\\)<br> \u9802\u70b9\u306e\u5ea7\u6a19\uff1a\\((-1,3)\\)<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\\(y=3x^{2}+6x-4\\)\u306e\u8ef8\u3068\u9802\u70b9<\/h3>\n\n\n\n<p>2\u6b21\u95a2\u6570\\(y=3x^{2}+6x-4\\)\u3092\u5e73\u65b9\u5b8c\u6210\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\\begin{eqnarray}<br>\ny&amp;=&amp;3x^{2}+6x-4\\\\<br>\n&amp;=&amp;3(x^{2}+2x)-4\\\\<br>\n&amp;=&amp;3\\{(x^{2}+2x+1)-1\\}-4\\\\<br>\n&amp;=&amp;3(x^{2}+1)^{2}-7<br>\n\\end{eqnarray}<\/p>\n\n\n\n<p>\u3057\u305f\u304c\u3063\u3066\u3001<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" width=\"550\" height=\"346\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2021\/05\/\u7df4\u7fd2\u554f\u984c2.png\" alt=\"\u9802\u70b9\u3068\u8ef8\u306e\u6c42\u3081\u65b9\u300a\u7df4\u7fd2\u554f\u984c\u300b\" class=\"wp-image-7560\" srcset=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2021\/05\/\u7df4\u7fd2\u554f\u984c2.png 550w, https:\/\/math-travel.jp\/wp-content\/uploads\/2021\/05\/\u7df4\u7fd2\u554f\u984c2-300x189.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-border -border01\">\u89e3\u7b54<br> \u653e\u7269\u7dda\u306e\u8ef8\uff1a\\(x=-1\\)<br> \u9802\u70b9\u306e\u5ea7\u6a19\uff1a\\((-1,-7)\\)<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\\(y=-2x^{2}-4x+5\\)\u306e\u8ef8\u3068\u9802\u70b9<\/h3>\n\n\n\n<p>2\u6b21\u95a2\u6570\\(y=-2x^{2}-4x+5\\)\u3092\u5e73\u65b9\u5b8c\u6210\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\\begin{eqnarray}<br>\ny&amp;=&amp;-2x^{2}-4x+5\\\\<br>\n&amp;=&amp;-2(x^{2}+2x)+5\\\\<br>\n&amp;=&amp;-2\\{(x^{2}+2x+1)-1\\}+5\\\\<br>\n&amp;=&amp;-2(x^{2}+1)^{2}+7<br>\n\\end{eqnarray}<\/p>\n\n\n\n<p>\u3057\u305f\u304c\u3063\u3066\u3001<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" width=\"597\" height=\"411\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2021\/05\/\u7df4\u7fd2\u554f\u984c3.png\" alt=\"\u9802\u70b9\u3068\u8ef8\u306e\u6c42\u3081\u65b9\u300a\u7df4\u7fd2\u554f\u984c\u300b\" class=\"wp-image-7561\" srcset=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2021\/05\/\u7df4\u7fd2\u554f\u984c3.png 597w, https:\/\/math-travel.jp\/wp-content\/uploads\/2021\/05\/\u7df4\u7fd2\u554f\u984c3-300x207.png 300w\" sizes=\"(max-width: 597px) 100vw, 597px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-border -border01\">\u89e3\u7b54<br> \u653e\u7269\u7dda\u306e\u8ef8\uff1a(x=-1)<br> \u9802\u70b9\u306e\u5ea7\u6a19\uff1a((-1,7))<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"matome\">2\u6b21\u95a2\u6570\u306e\u9802\u70b9\u30fb\u8ef8\u3000\u307e\u3068\u3081<\/h2>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" width=\"351\" height=\"205\" src=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2021\/05\/\u4e8c\u6b21\u95a2\u6570\u306e\u8ef8\u3068\u9802\u70b91.png\" alt=\"2\u6b21\u95a2\u6570\u306e\u8ef8\u3068\u9802\u70b91\" class=\"wp-image-5500\" srcset=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2021\/05\/\u4e8c\u6b21\u95a2\u6570\u306e\u8ef8\u3068\u9802\u70b91.png 351w, https:\/\/math-travel.jp\/wp-content\/uploads\/2021\/05\/\u4e8c\u6b21\u95a2\u6570\u306e\u8ef8\u3068\u9802\u70b91-300x175.png 300w\" sizes=\"(max-width: 351px) 100vw, 351px\" \/><\/figure>\n<\/div>\n\n\n<p><span class=\"huto\">\u4eca\u56de\u306f2\u6b21\u95a2\u6570\u306e\u8ef8\u3068\u9802\u70b9\u306e\u6c42\u3081\u65b9\u306b\u3064\u3044\u3066\u307e\u3068\u3081\u307e\u3057\u305f\u3002<\/span><\/p>\n\n\n\n<div class=\"swell-block-capbox cap_box\"><div class=\"cap_box_ttl\"><span>2\u6b21\u95a2\u6570\u306e\u8ef8\u30fb\u9802\u70b9\u307e\u3068\u3081<\/span><\/div><div class=\"cap_box_content\">\n<p><span class=\"huto\">2\u6b21\u95a2\u6570\u306e\u8ef8\u3068\u9802\u70b9<\/span><\/p>\n\n\n\n<p>2\u6b21\u95a2\u6570\\(y=a(x-p)^{2}+q\\)\u306e\u30b0\u30e9\u30d5\u306b\u304a\u3044\u3066\u3001<br>\u8ef8\u3000\\(x=p\\)\u3001\u9802\u70b9\u3000\\((p,q)\\)<\/p>\n\n\n\n<p><span class=\"huto\">\u8ef8\u3068\u9802\u70b9\u306e\u6c42\u3081\u65b9<\/span><\/p>\n\n\n\n<ul 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