题干

如图(1),直线y=﹣x+3与x轴、y轴分别交于点B、点C,经过B、C两点的抛物线y=x2+bx+c与x轴的另一个交点为A,顶点为P.

(1)求该抛物线的解析式;

(2)在该抛物线的对称轴上是否存在点M,使以C、P、M为顶点的三角形为等腰三角形?若存在,请直接写出所有符合条件的点M的坐标;若不存在,请说明理由;

(3)连接AC,在x轴上是否存在点Q,使以P、B、Q为顶点的三角形与△ABC相似?若存在,请求出点Q的坐标;若不存在,请说明理由;

(4)当0<x<3时,在抛物线上求一点E,使△CBE的面积有最大值.

(图(2)、图(3)供画图探究)

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答案(点此获取答案解析)

解:(1)由已知,得B(3,0),C(0,3),

3=c0=9+3b+

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Time for a Brainstorm

    A brainstorm is a session where a small group of people come together to solve a problem.People voice spontaneous ideas, sometimes just shouting , and a note-taker writes them all down.____By getting different ideas out there, ideas are said to bounce off each other and even can help solve the problem at hand.Brainstorming is often a group exercise but individuals can also conduct personal brainstorms.

    ____He defined it as using the brain to storm a creative problem and do so in commando (突击队)fashion,with each stormer attacking the same objective.According to him,, it was easier to tone down a wild idea than think up a new one.He placed importance on the collection of as many ideas as possible and dismissed scientific thinking.

    Brainstorming has become one of the most popular ways to solve problems and hold discussion in schools and businesses.Many students brainstorm for a group assignment or even for a personal essay. Sarah Grace, 24, is an Australian marketing analyst and uses brainstorming during all her creative duties. She thinks brainstorming is the best way to work as a team.The sessions get everyone on the same page,everyone moving together and with a clear understanding about the foundations of an event or idea.____

However, a big problem with brainstorming is creating a mess that leads people further away from a solution.____ If you don't have a strong moderator or leader of the brainstorm, can go really off track,and people just start discussing something totally different. Brainstorming can sometimes confuse the human brain. ____ If you brainstorm too much and your page is filled up with all the messy links, you can paint yourself into a bit of comer and get trapped with ideas. You need to move past brainstorming as soon as you have something workable.

A.The ideas can be smart,strange or crazy.

B.It is caused by a lack of direction from a leader.

C.Brainstorming really helps her organize her thoughts.

D.Brainstorming really is the best way to build team spirit.

E.It can open too many doors and not suggest a clear direction.

F.Brainstorms were popularized in the 1940s by American advertising boss Alex Osborn..

G.They can be words, phrases, paragraphs and anything that can help answer the question.