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歡迎您訪問數學考題練習:已知二次函數y=ax2+bx+c的圖象如圖所示!

數學考題練習:已知二次函數y=ax2+bx+c的圖象如圖所示

更新時間:2024-01-12 16:27:54作者:貝語網校

已知二次函數y=ax2+bx+c的圖象如圖所示,則當函數值為3時,自變量x的值為

A.3

B.4

C.-1

D.-1或3

試題答案

D

試題解析

利用對稱軸、頂點坐標、拋物線與x軸交點公式求出a、b、c的值,然后求當y=3時x的值.

解答:由圖象可知:=-1,

∵二次函數y=ax2+bx+c的圖象與坐標軸交于原點,

∴c=0,

∴b2=4a,

又∵二次函數y=ax2+bx+c的圖象與x的一個交點為(2,0),c=0,

∴4a+2b=0,

∴b2+2b=0,

解得:b=-2或b=0,

∵對稱軸x=1,

∴b=0不合題意,則b=2,

∴a=1,

則函數解析式為y=x2-2x,

當y=3時,x2-2x=3,

解得x=-1或3,故選D.

點評:數形結合法、假設法都是解決數學習題常用的方法,巧妙運用解題方法可以節省解題時間.

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