[{"data":1,"prerenderedAt":161},["ShallowReactive",2],{"topic-page:\u002Fhigh-school\u002Fmathematics-i\u002Fquadratic-functions\u002Fquadratic-functions-and-variable-relations":3},{"topic":4,"category":135,"seo":139,"breadcrumbs":144,"prerequisites":151,"nextTopics":152,"relatedTopics":160},{"id":5,"slug":6,"title":7,"summary":8,"canonicalPath":9,"categoryPath":10,"difficulty":11,"targetAudience":12,"estimatedMinutes":13,"generatedAt":14,"publishedAt":14,"updatedAt":14,"reviewStatus":15,"tags":16,"expectedKnowledge":21,"learningGoal":25,"blocks":26},"high-school-mathematics-i-quadratic-functions-quadratic-functions-and-variable-relations","quadratic-functions-and-variable-relations","二次関数と二つの数量","二次関数を、xとyという二つの数量の対応として捉えます。式の形だけでなく、表での変化や数量が取り得る範囲まで確認します。","\u002Fhigh-school\u002Fmathematics-i\u002Fquadratic-functions\u002Fquadratic-functions-and-variable-relations","\u002Fhigh-school\u002Fmathematics-i\u002Fquadratic-functions","beginner","student_high",5,"2026-07-27","ai_generated",[17,18,19,20],"数学I","二次関数","関数","数量の関係",[22,23,24],"比例と一次関数","文字式への代入","座標平面の基本","一方の値を決めると他方が決まる関係を表と式で読み、二次関数の候補を見分けられるようになる。",[27,32,41,51,57,78,84,94,100,116,125],{"id":28,"type":29,"title":7,"subtitle":30,"shortDefinition":31},"hero","HeroBlock","式の前に、何が何で決まるかを見る","一辺を決めると正方形の面積が決まるように、二つの数量には対応があります。二次関数は、その対応を二次式で表して変化を調べる道具です。",{"id":33,"type":34,"term":18,"definition":35,"plainExplanation":36,"keywords":37},"definition","DefinitionBlock","xの値を決めるとyの値が一つに決まり、yがxの二次式で表される関数です。","代表的な形は y=ax²+bx+c で、aは0ではありません。大切なのはx²という記号を見つけるだけではなく、xを何の量、yを何の量としているかを読むことです。長さや時間には現実に取り得る範囲があるので、式と一緒に条件も確認します。",[38,39,40],"入力xと出力y","aは0ではない","数量の範囲も確認",{"id":42,"type":43,"title":44,"points":45,"body":50},"key-points","KeyPointBlock","関係を読む3つの視点",[46,47,48,49],"xを決めるとyが一つに決まる","yはxの二次式で表される","同じ幅のxでもyの増え方は一定でない","単位と取り得る範囲を忘れない","式、表、場面は同じ関係の別の表し方です。一つだけで判断せず往復します。",{"id":52,"type":53,"src":54,"alt":55,"caption":56},"diagram","DiagramBlock","\u002Fassets\u002Fhigh-school\u002Fmathematics-i\u002Fquadratic-functions\u002Fquadratic-functions-and-variable-relations\u002Fvariable-relation.svg","正方形の一辺xと面積yを値の表に対応させた図","一辺xを1、2、3と増やすと、面積yは1、4、9になります。入力が同じ1ずつ増えても、面積の増え方は一定ではありません。",{"id":58,"type":59,"title":60,"lead":61,"formulas":62,"strategy":77},"formula","FormulaBlock","二次関数の一般形","二次の項が残る関数を扱います。",[63],{"label":64,"expression":65,"meaning":66,"symbols":67},"一般形","y = ax^2 + bx + c","a、b、cは定数で、aは0ではない。xを入れるとyが一つ決まる。",[68,71,74],{"symbol":69,"meaning":70},"x","入力する量",{"symbol":72,"meaning":73},"y","対応して決まる量",{"symbol":75,"meaning":76},"a","二次の変化を決める係数","場面では、まずxとyの意味を書いてから式へ代入します。",{"id":79,"type":80,"scenario":81,"explanation":82,"result":83},"example","ExampleBlock","一辺がx cmの正方形の面積をy cm²とする。","面積は一辺×一辺なので y=x² です。x=1ならy=1、x=2ならy=4、x=3ならy=9となります。xを1増やしたときのyの増加は3、5と変わるため、一定の割合で増える一次関数とは違います。また一辺の長さなので、現実の範囲はx>0です。","式だけでなく、表の変化とxの意味まで読むと、二次関数としての特徴が見えます。",{"id":85,"type":43,"title":86,"points":87,"body":93},"model-boundary","式だけでなく変数の意味までモデルに含める",[88,89,90,91,92],"どちらを自分で決める量xにするかを最初に書く","結果として決まる量yと、その単位を対応させる","表ではxの刻みだけでなくyの差がどう変わるかを見る","a=0なら二次の項が消えるため二次関数ではない","式・表・グラフが同じ対応を示すか具体的な値で検算する","同じ二次式でも、場面によって使えるxの範囲と単位が変わります。正方形の一辺ならxは正で、面積yは0より大きく、xがcmならyはcm²です。式が計算できる値と、場面で意味をもつ値を区別します。",{"id":95,"type":96,"warningTitle":97,"message":98,"severity":95,"action":99},"warning","WarningBlock","x²が見えるだけでは判断しない","式を展開・整理すると二次の項が消える場合や、xの取り得る範囲が場面で限られる場合があります。関係式を整理し、aが0でないことと数量の意味を確認します。","「何をxにし、何がyとして決まるか」を一文で言い直しましょう。",{"id":101,"type":102,"title":103,"questions":104},"quiz","QuizBlock","確認テスト",[105],{"question":106,"choices":107,"answerIndex":111,"choiceExplanations":112},"xを入力、yを出力とするとき、二次関数であるものはどれですか。",[108,109,110],"y=3x+2","y=x²-4x+1","y=6\u002Fx",1,[113,114,115],"xの次数が1なので一次関数です。","正解です。整理後もx²の項が残り、その係数は0ではありません。","xが分母にある反比例型で、二次式ではありません。",{"id":117,"type":118,"title":119,"points":120},"summary","SummaryBlock","まとめ",[121,122,123,124],"二次関数は二つの数量の対応","一般形ではaは0でない","式・表・場面を往復して読む","単位と定義域も関係の一部",{"id":126,"type":127,"title":128,"nextTopics":129,"relatedKeywords":131},"next-action","NextActionBlock","次は基本の放物線へ",[130],"high-school-mathematics-i-quadratic-functions-graph-of-y-equals-ax-squared",[132,133,134],"**放物線**","係数a","軸と頂点",{"path":10,"title":18,"description":136,"parentPath":137,"accentToken":138},"二次関数の値の変化、グラフ、最大・最小、二次方程式・二次不等式との関係を整理していくカテゴリです。","\u002Fhigh-school\u002Fmathematics-i","signal-blue",{"title":140,"description":141,"canonicalUrl":142,"ogImage":143},"二次関数と二つの数量 | 数学I","高校数学Iの二次関数を、入力と出力、値の表、身近な面積の例から初学者向けに学びます。","https:\u002F\u002Fzeqnilo.com\u002Fhigh-school\u002Fmathematics-i\u002Fquadratic-functions\u002Fquadratic-functions-and-variable-relations","https:\u002F\u002Fzeqnilo.com\u002Fassets\u002Fsite\u002Fdefault-og.svg",[145,148,149,150],{"title":146,"path":147},"高校","\u002Fhigh-school",{"title":17,"path":137},{"title":18,"path":10},{"title":7,"path":9},[],[153],{"id":130,"title":154,"summary":155,"canonicalPath":156,"categoryPath":10,"categoryTitle":18,"difficulty":11,"targetAudience":12,"estimatedMinutes":13,"publishedAt":14,"updatedAt":14,"reviewStatus":15,"tags":157},"y=ax² のグラフ","原点を頂点とする放物線を表から描き、係数aの符号と絶対値が開く向き・広がりに与える影響を整理します。","\u002Fhigh-school\u002Fmathematics-i\u002Fquadratic-functions\u002Fgraph-of-y-equals-ax-squared",[17,18,158,159],"放物線","グラフ",[],1785565323055]