According to the actual situation which can be seen in the graph, we can get ，
Therefore ， . And we already know that the coordinates of B is , so ＝4. Therefore, the coordinates of point B is B(4,4).
(2) On the hill line AB, ，so we can get . Taken ，we can get . And taken ，we can get . Therefore, the length of the first step is hectometers centimeters. In the similar way, taken and ，we can get and . Therefore, the length of the second step is hectometers meters and the length of the third step is hectometers centimeters.
As for the second question, we already know the point , and ，so . However, . It has been told that the length can’t be less than 20centimeters. Therefore, we can get the conclusion that these steps can't be spread from the mountaintop to the point B. That is to say, they can't be spread to the bottom of the hill.
（3）According to the quadratic functions and , we can get the coordinates of the following points: , , and . As the graph has shown, only when the cableway is over the line BC, the impending height of the cableway is likely to get the maximum value. When the cableway is over the line BC, its impending height is the difference between these two functions which can be expressed like this:
When ，
Therefore, the maximum value of the cableway’s height is meters．
The above problems can be usually involved in the construction of mountain tourism, and they are typical cases of the application of quadratic functions in the engineering construction. The general steps to solve the problem of function application are: first, change the actual problem into a mathematical problem. And second, establish the corresponding mathematical model of a quadratic function based on mathematical knowledge and try to solve the mathematical model. At last, restore the result which is achieved by mathematical methods to the practical problem and make sure that the result conforms to the actual situations.
Mathematics is a very practical subject. People come to have a good understanding of math at the same time as trying to know about and changing the world since the appearance of human beings. At present, mathematical knowledge and ideology has been applied broadly in industrial and agricultural production and human’s daily life. In this paper, the quadratic function, a common mathematical model which is very closely related with our life, is focused on and a simple example about the solution of a practical problem is listed to prove the application of the quadratic function in the engineering construction. And it is concluded that the key to solve the practical problem by the way of a quadratic function is to translate the problem into a mathematical question and try to build up the corresponding mathematical model.
References 文献
Zhang, Z. (2011). Sobolev seminorm of quadratic functions with applications to derivative-free optimization. Mathematical Programming, 1-20.
Fletcher, R. (2013). Practical methods of optimization. John Wiley & Sons.
