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问题 解答题

已知抛物线y=-x2+bx+c，它与x轴的两个交点分别为（-1，0），（3，0），求此抛物线的解析式．

答案

根据题意得，

-1-b+c=0
-9+3b+c=0
，

解得

b=2
c=3
，

∴抛物线的解析式为y=-x2+2x+3；

或：由已知得，-1、3为方程-x2+bx+c=0的两个解，

∴-1+3=b，（-1）×3=c，

解得b=2，c=3，

∴抛物线的解析式为y=-x2+2x+3．

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