如图,二次函数y=ax2+bx+c(a≠0)的图象过点(﹣1,2),且与x轴交点的横坐标为x1、x2,其中﹣2<x1<﹣1,0<x2<1,则下列结论:①2a﹣b<0,②4a﹣2b+c>0,③b2+8a>4ac,④当x>0时,函数值随x的增长而减少,⑤a+c<1.其中正确的是_____ (填序号).
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/3/d52392c9-f911-44ce-baba-0d55ab95e399.png?resizew=125)
更新时间:2021-05-07 13:37:53
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【知识点】 根据二次函数的图象判断式子符号解读
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【推荐1】如图,二次函数
的图象与x轴交于A,B两点,与y轴交于点C,点A坐标为
,点C在
与
之间
不包括这两点
,抛物线的顶点为D,对称轴为直线
有以下结论:
①
;
②![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c766352f0be38b719621052de92615bd.png)
③ 若点
,点
是函数图象上的两点,则
;
④
;⑤
可以是等腰直角三角形.
其中正确的结论序号为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0284f7c00dc23c25dc35ad5335f3ffd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb7bf121f4980e3378157ceaecf98b0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44a7da9439e0ed89968ff915e6e96171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679e086f6642c493189402aeb960cbd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de629ae869e25cbd394121fc990d2f85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0ef244e9cd295656496929fbb46a9a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20bdcbc39ebe0763c44edde93cf71ed2.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bbc1d6a66b5583e556fbf194164b068.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c766352f0be38b719621052de92615bd.png)
③ 若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/153096f4e1edcf08ea01e3f815bce113.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd72ba841f0a7f485104cc7b9b7153fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4514bbb120c729b9919e987537ff910f.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23989b00390aa1212cc533c94cc820dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/591b671d0b58dde70454388e7ae8c0d0.png)
其中正确的结论序号为
![](https://img.xkw.com/dksih/QBM/2020/11/5/2586534848667648/2588551725809664/STEM/43823b356d1e4080881f6ebfe3ac54d6.png?resizew=141)
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【推荐2】已知二次函数
(
为常数,
)的图象开口向下,对称轴为直线
,且与
轴的一个交点在点(-1,0),(0,0)之间,下列结论正确的是________ (填写序号).
①
;②
;③
(m是一个常数);④若方程
(m是一个常数)的根为
,则
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a90385c676848de67293e3ed6bc000fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b5ccc34de572fab89b56f129b624dc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ad3865686e43b90827a31a35657b3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd2336e50c0afb3e8e73a6ea9070ded.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85db04ca5ad0f820ebbb12ba52b54be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/020f4ca40c0483daacdcc95ba03dfa94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56a7a9c21d44c55fb211ed0dec84bce7.png)
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