题干

如图,在直角坐标系中,点P的坐标是(n,0)(n>0),抛物线y=﹣x2+bx+c经过原点O和点P.已知正方形ABCD的三个顶点为A(2,2),B(3,2),D(2,3).

(1)求c,b并写出抛物线对称轴及y的最大值(用含有n的代数式表示);

(2)求证:抛物线的顶点在函数y=x2的图象上;

(3)若抛物线与直线AD交于点N,求n为何值时,△NPO的面积为1;

(4)若抛物线经过正方形区域ABCD(含边界),请直接写出n的取值范围.

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答案(点此获取答案解析)

解:(1)把x=0,y=0代入y=﹣x2+bx+c,得c=0.

再把x=n,y=0代入y=﹣x2+bx,

得﹣n2+bn=0.

∵n>0,

∴b=n.

∴y=﹣x2+nx=﹣(x﹣n2

同类题4

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(节选自《明史•杨维桢传》)

同类题5

根据短文理解,选择正确答案。

    Andy never wanted to go to bed on time. His parents had explained to him how important it was to go to bed early and get a good rest. But Andy paid no attention to them, and they didn't know what to do until one weekend when they were visiting Andy's grandparents.

    Grandpa Peter heard all about it and said, "This sounds like a job for Tubby." So Andy's parents loaded the cat onto the car and returned home.

That night, at bedtime, the same problem happened. Andy didn't want to go to bed, and even though his parents waited a while to see if Tubby would solve the problem, nothing happened.

    Hours later, Andy finally decided to go to bed. But what a surprise when he entered his bedroom! Tubby was in his bed, totally sprawling out, pot-belly in the air, and snoring like an express train.

    Andy tried to move the cat, but there was no way of moving him an inch. That night he hardly slept, lying on one tiny corner of his bed.

    The next day the same thing happened, even though Andy was much more tired from not having slept well. When the third day arrived, he had understood that if he wanted to sleep in his bed, he would have to get into it before Tubby did. That night, when his parents only started to mention the topic of bedtime, Andy rushed upstairs and dived into bed. His parents could not believe it. They knew nothing about Tubby in the bed, nor did they understand why Andy went to bed on time without complaint. They were so happy about this that they stayed up quite late, celebrating.