1 . 已知,关于x 的二次函数
.
(1)若函数
经过点
,求抛物线的对称轴;
(2)若点
均在抛物线
上,则p q(填“
”,“
”或“
”).
(3)记
,当
时,
始终成立,求t 的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e60cd7debbcc4ac5475e8bd5bb60b7.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e60cd7debbcc4ac5475e8bd5bb60b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32f19b11843421f6082d3aef4115ddd6.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7b71e5943c4a4d00a1f367fe90553aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e60cd7debbcc4ac5475e8bd5bb60b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/392cdb9d30684cce244bef94b8d861b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff7942da6c3fc4005256fb1458557c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6706fe00b4e231e62d9ecbec567d526b.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac11db435fe89dc3edfabe9ccd5680a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47b6fd5a1dbb65cbe9bfe602c914a24f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e1113e9b568fb9ca3286582368e257a.png)
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2 . 已知二次函数
(t为常数),点
、
是其图象上两点,若
,则
的取值范围为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c9a0fd25f31c20d7b23dc8c0b39fb84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe7bce26112f3c9441686d2268192a31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0a44c195e646b199b7247fa715e914d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f99df1a7b58018125b99578b779342.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450398974b1561ca801e102e16df6789.png)
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名校
3 . 在平面直角坐标系
,
是抛物线
上任意两点,设抛物线的对称轴为直线
.
(1)若
,
,求
的值;
(2)若
,
,当
时,
,当
时,
,求
的值;
(3)若对于
,
,都有
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/311a36f03fac6d979014e605e80913a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23d046826b3840b908d823d90be499e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd69aebdafb31468eb13ce3b28a36e47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6f7b16d65f1b2b8bea8cf4a83fde925.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c4223bd6ee8f82d59d244371fbcddc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7389956fef69001377e48f01af71af8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/204e5160ff110a19878e4fae639319e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27dfd40d48b5297df3d3c1fddc431313.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a79d7f73b6128650bf7aed538260c72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b21a6817fd5ddc56f0295109a2be6ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56ef88280301b355d6d68f08798d7b22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/951a1aedd0ef2913cf0a06b86573ce5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ae2496865059425488e90e0bc7dddd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f99df1a7b58018125b99578b779342.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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4 . 二次函数
(
,且a,b为常数),当
或
时
.
(1)求m和b的值:
(2)当
时,
,求a的取值范围:
(3)若该二次函数图象经过点
,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e431b3348828c95511bfc0be89db9ce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c50866229ec5a3640fb250f9bd2192b3.png)
(1)求m和b的值:
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97449fb669ca2b345d21aa870e795e58.png)
(3)若该二次函数图象经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6933978223d24fae0e083568d5fa0c38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4938f074e1f859f88508f1294473d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f68b27726a0c1a272ca9f40c6f42063.png)
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5 . 已知点
和点
都在抛物线
上.
(1)若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
______ ;
(2)若
,则k的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a12e370f5ae4416c62a6c44ccc77c47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177d06ed0f1f470b446785981f090e80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25d66d8fff2fca0b9a8d49821c6842a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1292c47f62023b747f1a4bd615c75284.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfceface585716e79a1225167e08564e.png)
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名校
6 . 如图,已知二次函数
的图象经过点
和
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/7/9efecd80-b380-490a-ad7d-1598ecf00848.png?resizew=134)
(1)求该二次函数的表达式及图象的顶点坐标.
(2)当
时,请根据图象直接写出x的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e59da5115d0dafea24822245f92c48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25059a7a9c09947e44aa1f957dc79ba5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3c9cc823b331f0c211c1541d9bdb62.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/7/9efecd80-b380-490a-ad7d-1598ecf00848.png?resizew=134)
(1)求该二次函数的表达式及图象的顶点坐标.
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ea60e346b9c8664e29ff53e5237dbb.png)
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7 . 如图,已知二次函数图象经过点
和
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/25/f62b64ab-db27-4daa-abf8-597462ca8cae.jpg?resizew=130)
(1)求该二次函数的表达式及图象的顶点坐标.
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be13a13be9ef147943fbdc142ebbc098.png)
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8 . 在平面直角坐标系中,直线
与
交于点
,则不等式
的解集为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4357446255703313abc3fc7ee057c1dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70053ce3897b3499976031624c905782.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0924ff22fff9f5639feb0ceeece80d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f39f82226be73ed35ba0c572e8c4d154.png)
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9 . 在平面直角坐标系
中,已知点
,
在二次函数
的图象上.
(1)当
时,求
的值;
(2)在(1)的条件下,当
时,求
的取值范围;
(3)若
时,函数的最小值为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e59bdeeea8ca6f2c5c49e4ed8b5338d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2e0d69a73b6134bcc170b07c8af3515.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/974cf6ed500e27d2a9928db300645f4f.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0a4480988244a9d04ec293975db2cc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)在(1)的条件下,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38f2333e2a05532b97e14b912e331ec6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a12a30935c79ae769818043a496f53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d13ce3ebd1112220c639562739f1f9d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd1f0ace9ca0b79929e73af6c201c2e.png)
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名校
10 . 已知二次函数
(
)的图像经过点.
和
.
(1)求
,
满足的关系式;
(2)若函数图像与
轴无交点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a90385c676848de67293e3ed6bc000fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/568e896d0cbf54daddec08afaf7e1aff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5590337b3868db8523eeb7f448efcf05.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)若函数图像与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c925be255ca736a53b24d13ddede1a86.png)
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