こんにちは。高校数学の定期テストでよく見かける二次関数の符号決定などの解法を書いておきます。例題を解きながら見ていきましょう。
【例】二次関数のグラフが次のように表されるとき,
の符号を求めなさい。
【解法】
![Rendered by QuickLaTeX.com a, c, b^2-4ac, a+b+c, a-b+c, b](https://mathtext.info/blog/wp-content/ql-cache/quicklatex.com-fef2720cd6cbada63f02f1081539d911_l3.png)
![Rendered by QuickLaTeX.com a>0](https://mathtext.info/blog/wp-content/ql-cache/quicklatex.com-2eed4f2758f118933a70ef7a7f291f74_l3.png)
![Rendered by QuickLaTeX.com c<0](https://mathtext.info/blog/wp-content/ql-cache/quicklatex.com-a4331badc9c17332448486c7091085cb_l3.png)
![Rendered by QuickLaTeX.com f(0)=c](https://mathtext.info/blog/wp-content/ql-cache/quicklatex.com-d1df66b644fa8b946dea12ef1fef816d_l3.png)
![Rendered by QuickLaTeX.com y](https://mathtext.info/blog/wp-content/ql-cache/quicklatex.com-5d76ceac31cb52dd9eb4431a14c502dc_l3.png)
![Rendered by QuickLaTeX.com c](https://mathtext.info/blog/wp-content/ql-cache/quicklatex.com-4b0923aa4784625c1c704c5edfbd409a_l3.png)
![Rendered by QuickLaTeX.com y](https://mathtext.info/blog/wp-content/ql-cache/quicklatex.com-5d76ceac31cb52dd9eb4431a14c502dc_l3.png)
![Rendered by QuickLaTeX.com b^2-4ac>0](https://mathtext.info/blog/wp-content/ql-cache/quicklatex.com-06811d073234b3ffbe1f039f09e51a39_l3.png)
![Rendered by QuickLaTeX.com x](https://mathtext.info/blog/wp-content/ql-cache/quicklatex.com-5f16b0dcec027c9742e11d99170299a8_l3.png)
![Rendered by QuickLaTeX.com D=b^2-4ac>0](https://mathtext.info/blog/wp-content/ql-cache/quicklatex.com-244793aa64ab52dc3cccd0391a0d5706_l3.png)
![Rendered by QuickLaTeX.com a+b+c<0](https://mathtext.info/blog/wp-content/ql-cache/quicklatex.com-89bfc516b8bbed63cbc2805ab08d208e_l3.png)
![Rendered by QuickLaTeX.com f(1)=a+b+c](https://mathtext.info/blog/wp-content/ql-cache/quicklatex.com-8a2ebfd1d1081b850ddf29bab55d4a85_l3.png)
![Rendered by QuickLaTeX.com x=1](https://mathtext.info/blog/wp-content/ql-cache/quicklatex.com-8a4b1fabb9dd2ab5aece4bfdff8f5021_l3.png)
![Rendered by QuickLaTeX.com a-b+c>0](https://mathtext.info/blog/wp-content/ql-cache/quicklatex.com-a26d0fe54c61ff747db3ccd8d3cc9825_l3.png)
![Rendered by QuickLaTeX.com f(-1)=a-b+c](https://mathtext.info/blog/wp-content/ql-cache/quicklatex.com-fabefa4d1e482a06bfc9f51d3bf1bf5c_l3.png)
![Rendered by QuickLaTeX.com x=-1](https://mathtext.info/blog/wp-content/ql-cache/quicklatex.com-7edba747bcbd8a68875d9a9268b1c527_l3.png)
![Rendered by QuickLaTeX.com b<0](https://mathtext.info/blog/wp-content/ql-cache/quicklatex.com-058fb7849bb54de8d2ffde05ed5d33de_l3.png)
![Rendered by QuickLaTeX.com b](https://mathtext.info/blog/wp-content/ql-cache/quicklatex.com-7d3b74b93cf8d3562b537c81c243a48c_l3.png)
![Rendered by QuickLaTeX.com f(x)=ax^2+bx+c](https://mathtext.info/blog/wp-content/ql-cache/quicklatex.com-0aaf8ee3e465ffeba2548f2295c54b53_l3.png)
![Rendered by QuickLaTeX.com f(x)=a\left(x+\dfrac{b}{2a}\right)-\dfrac{b^2}{4a}+c](https://mathtext.info/blog/wp-content/ql-cache/quicklatex.com-1ba51e74d01ffdeee53159c24dd78924_l3.png)
軸は
![Rendered by QuickLaTeX.com x=-\dfrac{b}{2a}](https://mathtext.info/blog/wp-content/ql-cache/quicklatex.com-6f4e7efc4a64dd41e8fd9b77dd470550_l3.png)
この軸の符号はグラフから正
![Rendered by QuickLaTeX.com \left(-\dfrac{b}{2a}>0\right)](https://mathtext.info/blog/wp-content/ql-cache/quicklatex.com-05ac7f406c8927b0ce6d8dcacc1979ad_l3.png)
![Rendered by QuickLaTeX.com a>0](https://mathtext.info/blog/wp-content/ql-cache/quicklatex.com-2eed4f2758f118933a70ef7a7f291f74_l3.png)
![Rendered by QuickLaTeX.com b](https://mathtext.info/blog/wp-content/ql-cache/quicklatex.com-7d3b74b93cf8d3562b537c81c243a48c_l3.png)
![Rendered by QuickLaTeX.com b<0](https://mathtext.info/blog/wp-content/ql-cache/quicklatex.com-058fb7849bb54de8d2ffde05ed5d33de_l3.png)
以上このようにして求めます。
軸を求めるとき, 平方完成が面倒なら軸の式
![Rendered by QuickLaTeX.com x=-\dfrac{b}{2a}](https://mathtext.info/blog/wp-content/ql-cache/quicklatex.com-6f4e7efc4a64dd41e8fd9b77dd470550_l3.png)
符号決定
グラフの概形をしっかり読み取って, 符号を決定しよう。はグラフが上に凸か下に凸かで符号が決まる。
はグラフと
軸との交点の符号で決まる。
の符号は軸で決めることが多いので, 軸の式
をしっかり覚えておこう。