如图,已知点A(﹣1,0),B(4,0),点C在y轴的正半轴上,且∠ACB=90°,抛物线y=ax2+bx+c经过A、B、C三点,其顶点为M.
如图,边长分别为2和4的两个全等三角形,开始它们在左边重叠,大△ABC固定不动,然后把小△A′B′C′自左向右平移,直至移到点B′到C重合时停止,设小三角形移动的距离为x,两个三角形的重合部分的面积为y,则y关于x的函数图象是( )
阅读下面短文, 从每小题所给的A、B、C、D四个选项中选出最佳选项。
According to a book survey by online bookstore Dangdang, the following four books are the most popular among students.
The Little Prince
Writer: Antoine de Saint-Exupéry
Price: $9. 99
Overview: The little prince lives alone on his little planet, but one day he leaves his planet and travels on the earth. In the travel, the little prince saw different kinds of unhappy people and finally learned about love.
The Adventures of Pinocchio
Writer: Carlo Collodi
Price: $3. 99
Overview: It’s about the naughty adventures of Pinocchio and his poor father. An angel gives life to Pinocchio, so that he starts his adventures. Once he tells a lie, his nose would be longer. After the adventures, Pinocchio finally grows up.
Peter Pan
Writer: James Matthew Barrie
Price: $8. 99
Overview: The writer uses Neverland and the boy Peter Pan who hates to grow up to tell people that childhood is the most beautiful music of our life and children have the right to enjoy the happiness of their childhood.
Alice Adventures in Wonderland
Writer: Lewis Carroll
Price: $7. 99
Overview: It tells the story of a young girl named Alice, who follows a rabbit entering a magical world called Wonderland. She has many unusual experiences. It is one of the most loved children’s books of all time, and many adults enjoy it as well.
已知a是最大的负整数,b是多项式2m2n﹣m3n2﹣m﹣2的次数,c是单项式﹣2xy2的系数,且a、b、c分别是点A、B、C在数轴上对应的数.
(1)求a、b、c的值,并在数轴上标出点A、B、C.
(2)若动点P、Q同时从A、B出发沿数轴负方向运动,点P的速度是每秒12个单位长度,点Q的速度是每秒2个单位长度,求运动几秒后,点Q可以追上点P?
(3)在数轴上找一点M,使点M到A、B、C三点的距离之和等于10,请直接写出所有点M对应的数.(不必说明理由).