1958 AMC 12 第 22 题

Question

将一个质点放在抛物线

y=x^2-x-6

上纵坐标为

6

的点

P

处。让它沿抛物线滚动，直到到达纵坐标为

-6

的最近点

Q

。质点移动的水平距离，即

P

与

Q

横坐标之差的绝对值，为：

A particle is placed on the parabola

y=x^2-x-6

at a point

P

whose ordinate is

6.

It is allowed to roll along the parabola until it reaches the nearest point

Q

whose ordinate is

-6.

The horizontal distance traveled by the particle (the numerical value of the difference in the abscissas of

P

and

Q

) is:

5

4

3

2

1

分别求抛物线上纵坐标为

6

和

-6

时的两个

x

坐标

Find the two

x

-coordinates where the parabola has ordinate

6

and the two where it has ordinate

-6

将每个上方点与同一分支上较近的下方点配对

Pair each upper point with the nearer lower point on the same branch

当

y=6

时，

x^2-x-12=0\text{，}

所以

x=4

或

-3

。当

y=-6

时，

x^2-x=0

，所以

x=0

或

1

。离

x=4

其他年份的第 22 题