题目

如图，点A，B，C都在抛物线y=ax2﹣2amx+am2+2m﹣5（其中﹣＜a＜0）上，AB∥x轴，∠ABC=135°，且AB=4．（1）填空：抛物线的顶点坐标为 （用含m的代数式表示）；（2）求△ABC的面积（用含a的代数式表示）；（3）若△ABC的面积为2，当2m﹣5≤x≤2m﹣2时，y的最大值为2，求m的值． 答案：【答案】（1）（m，2m﹣5）；（2）S△ABC =﹣；（3）m的值为或10+2．【解析】（1）利用配方法将二次函数解析式由一般式变形为顶点式，此题得解；（2）过点C作直线AB的垂线，交线段AB的延长线于点D，由AB∥x轴且AB＝4，可得出点B的坐标为（m＋2，4a＋2m−5），设BD＝t，则点C的坐标为（m＋2＋t，4a＋2m−5−        Domestic(驯养的) horses now pull ploughs, race in the Kentucky Derby, and carry police, But early horses weren’t tame(驯服的)enough to perform these kinds of tasks. Scientists think the first interactions ( 相互影响  interact   交流。合作)humans had with horses were far different from those today.        Thousands of years ago, people killed the wild horses that lived around them for food. Over time ,people began to catch the animals and raise them. This was the first step in domestivation.        As people began to tame and ride horses, they chose to keep those animals that had more desirable（可取的） characteristics（特征）. For example, people may have chosen to keep horses that had a gentle personality so they could be ridden more easily. People who used horses to pull heavy loads would have chosen to keep stronger animals . Characteristics like strength are partly controlled by the animals’ genes（基因）。So as the domesticated horses reproduced, they passed the characteristics on to their young. Each new generation of horses would show more of these chosen characteristics.        Modern-day horse breeds（品种） come in a wide variety of shapes and sizes. This variety didn’t exist in the horse population before domestication.The Shetland horse is one of the smallest breeds-----typically reaching only one meter tall. With short, strong legs, the animals were bred（繁殖） to pull coal out of mine shafts(矿井)with low ceilings. Huge horses like the Clydesdale came on the scene around 1700. People bred these heavy, tall horses to pull large vehicles used for carrying heavy loads.        The domestication of horses has had great effects on societies. For example , horses were important tools in the advancement of modern agriculture. Using them to pull ploughs and carry heavy loads allowed people to farm efficiently. Before they were able to ride horses, humans had to cross land on foot . Riding horses allowed people to travel far greater distances in much less time. That encouraged populations living in different areas to interact with one another. The new form of rapid transportation helped cultures spread around the world. 1. Before domestication horses were ______________.        A. caught for sports       B. hunted for food        C. made to pull ploughs D. used to carry people 2. The author uses the Shetland horse as an example to show_____________.        A. it is smaller than the Clydesdale horse        B. horses used to have gentle personalities        C. some horses have better shapes than others        D. horses were of less variety before domestication 3. Horses contributed to the spread of culture by__________.        A. carrying heavy loads        B. changing farming methods        C. serving as a means of transport        D. advancing agriculture in different areas 4. The passage is mainly about____________.        A. why humans domesticated horses        B. how humans and horses needed each other        C. why horses came in different shapes and sizes        D. how human societies and horses influenced each other