已知二次函數(shù)
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有兩個(gè)零點(diǎn)
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和
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,且
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最小值是
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,函數(shù)
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與
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的圖象關(guān)于原點(diǎn)對(duì)稱;
(1)求
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和
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的解析式;
(2)若
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在區(qū)間
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上是增函數(shù),求實(shí)數(shù)
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的取值范圍。
試題分析:解 (1) 依題意 設(shè)
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圖象的對(duì)稱軸是
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即
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得
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
(3分)
由函數(shù)
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的圖象與

的圖象關(guān)于原點(diǎn)對(duì)稱
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(5分)
(2)由(1)得
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(6分)
①當(dāng)
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時(shí),
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滿足在區(qū)間
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上是增函數(shù) (8分)
②當(dāng)
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時(shí),
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圖象對(duì)稱軸是
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則
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,又
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解得
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(10分)
③當(dāng)
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時(shí),同理 則需
又
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解得
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(12分)
綜上滿足條件的實(shí)數(shù)
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的取值范圍是
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(14分)
點(diǎn)評(píng):解決的關(guān)鍵是利用二次函數(shù)的圖形與性質(zhì)來(lái)解決,屬于基礎(chǔ)題。
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
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
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(本題滿分12分)
已知二次函數(shù)
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滿足

且

.
(Ⅰ)求

的解析式;
(Ⅱ)當(dāng)
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時(shí),不等式:
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恒成立,求實(shí)數(shù)

的范圍.
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