问题 解答题

已知:抛物线y=x2-2mx+m2+2m-1,随着m取值的不同,抛物线的顶点坐标也将发生变化,请你通过计算说明,不论m取任何实数,抛物线的顶点都在一条固定的直线上.

答案

设抛物线的顶点坐标为(x,y),

由y=x2-2mx+m2+2m-1=(x-m)2+2m-1,

∴抛物线的顶点坐标为(m,2m-1),

即x=m,y=2m-1,

消去m得,y=2x-1,

即抛物线的顶点都在一条固定的直线y=2x-1上.

单项选择题
单项选择题

The largest earthquake (magnitude里氏9.5 ) of the 20th century happened on May 22, 1960 off the coast of South Central Chile.

It generated (生成) one of the most destructive Pacific-wide tsunamis (海啸). Near the

generating area, both the earthquake and the tsunami were very much destructive, particularly in the coastal area from Concepcion to the south end of Isla Chiloe. The largest tsunami damage occurred at Isla Chiloe-the coastal area closest to the epicenter(震中). Huge tsunami waves measuring as high as 25 meters arrived within 10 to 15 minutes after the earthquake, killing at least two hundred people, sinking all the boats, and flooding half a kilometer inland.

There was large damage and loss of life at Concepcion, Chile’s top industrial city. Near the city of Valdivia, the earthquake and following aftershocks generated landslides which killed 18 people. At the port city of Valparaiso, a city of 200,000, many buildings collapsed. A total of 130,000 houses were destroyed--one in every three in the earthquake zone and nearly 2,000,000 people were left homeless.

Total damage losses, including to agriculture and to industry, were estimated(估计) to be over a half billion dollars. The total number of deaths related with both the tsunami and the earthquake was never found accurately for the region. Estimates of deaths reached between 490 to 5,7002 with no distinction(差别) as to how many deaths were caused by the earthquake and how many were caused by the tsunami. However, it is believed that most of the deaths in Chile were caused by the tsunami.

What is generally thought the main cause of deaths in Chile()

A. Landslides.

B. The tsunami.

C. Aftershocks.

D. The magnitude 9.5 earthquake.