问题 解答题

自变量为x的二次函数y=ax2+(6a-2)x+9a-7(a>0).

(1)若a=1,-4≤x≤3,求函数值y的最大值与最小值;并分别指出所对应的自变量x的值;

(2)当a变化时,该二次函数图象是否经过定点?若是,请求出定点坐标;若不是,请说明理由;

(3)若该二次函数图象与x轴有两个不同的交点,而且两交点的横坐标均小于-1,求a的取值范围.

答案

(1)y=x2+4x+2=(x+2)2-2

因为-4≤x≤3,开口向上,对称轴x=-2

所以当x=-2时,有最小值-2,当 x=3时,有最大值23.

(2)将二次函数整理成y=a(x2+6x+9)-2x-7

令x2+6x+9=0⇒x=-3,将x=-3代入,则y=-1

经过验证点(-3,-1)满足函数表达式,所以该二次函数图象经过一个定点,坐标为(-3,-1).

(3)由(2)的结论,再由开口向上,可以知道该二次函数图象必与x轴有两个交点,

将x=-1代入表达式,得到相应的函数值为4a-5,要想两交点的横坐标均小于-1,只需要4a-5>0

所以a>

5
4

完形填空
阅读下面的短文,然后从A-F选项中,为每一小段选择合适的标题, 并把答案写在答案卷上。
A. The most common problem is a “wandering” mind
B. Selective listening is also a mental barrier
C. Listening isn’t an easy skill to master
D. Attitude can also influence good listening
E. Noise and background music makes listening more difficult
F. Listening is also related to the level of the listener’s knowledge
小题1:_____________
Listening is not as easy as someone thought. Even good listeners may recall only fifty percent of what they hear. Retention, the ability to remember and recall information, decreases about twenty to twenty-five percent after a few days. So no matter how well you listen in class, you’re always going to have to refresh your memory before a test! Unfortunately, many people have poor listening habits, and little listening training. To improve your listening skills, it’s important to understand what causes poor listening.
小题2:___________
If you find it difficult to concentrate solely on what a speaker is saying, there’s a good reason. The mind processes information much faster than a speaker can speak. The brain can process over 500 words per minute, while the average speaker talks at a rate of 124 to 250 words per minute. That means the mind can hear what’s being said and can think about something else at the same time.
小题3:____________
If you have a negative idea about the speaker or the topic, you’ll find it difficult to listen attentively. Hostile or captive audiences often have more difficultly listening than do favorable or voluntary ones.
小题4:____________
If a speaker speaks “above the heads” of an audience, people find it difficult to concentrate. Speakers who use unfamiliar words or who use incomplete explanations make it more difficult to listen. Speakers who “speak down” to audiences, failing to acknowledge what the audience already knows, also create mental blocks.
小题5:___________
When people listen selectively, they simply block out what they don’t want to hear. For instance, many people have habits that are dangerous to their health, like smoking. However, they often choose to block out what a speaker says about health risks. They may listen to a speech and think that the speaker’s message applies to other people, not them. In other words, they hear what they want to hear and ignore what they don’t want to hear.
问答题 简答题