The first term that I come to know about IB Mathematics is Quadratic. A quadratic equation is a second-order polynomial equation in a single variable x. According to Zhang (2011), a quadratic function is an important mathematical model to describe the relationship between variables in the real world and also the optimized model for a certain univariate. In the study of quadratic functions, we can get to know its broad connections and application values in each aspect of math. A function originates from the real life which also serves for the reality in return. Since the quadratic function is closely related with the actual life, it seems very significant to solve problems in the real world by the way of the quadratic function. The key is how to translate the actual problems into mathematical questions. (Fletcher, 2013)
二次功能已被广泛应用于建筑行业。 （Belegundu＆Tirupathi，2011）在本文中，我们将讨论通过二次函数解决工程中的实际问题的极端。当我们解决这个问题的时候，我们可以尝试把关于实际问题的极端问题变成一个关于二次函数极值的问题，然后通过求解二次函数的方法得到答案。无论如何，我们需要意识到这个问题。以下是旅游项目建设中二次函数的简单应用实例。Quadratic function has been widely used in the actual production and life especially in the engineering construction. (Belegundu & Tirupathi, 2011) In this paper we are going to discuss the extremum in solving practical problems in engineering construction by the way of quadratic function. When we solve the problem, we can try to change the question about extremum of the actual problem into question about the extremum of a quadratic function, and then get the answer by the method of solving quadratic function. Moreover, we must pay attention to that the answer should conform to the need of actual problem. The following is a simple application example of quadratic function in tourism project construction.
The problem is listed as follows. A tourist resort wants to develop a mountain landscape. As measured from the side of the mountain，the head on hillside line ABC is composed of two segments of parabolas in the same plane. The parabola AB goes downwards with point A as its vertex, and the parabola BC goes upwards with point C as its vertex. Take the horizontal line at the foot of the mountain (point C) as the X axis, and take the plumb line across the top of the mountain (point A) as the Y axis to set up rectangular plane coordinate system as shown in the graph (Unit: hundreds of meters). Given the analytic expression of AB parabola is , the analytic expression of BC parabola is , and point .
(1) Assume that is an arbitrary point on the line AB, and y represents x. Solve the coordinates of point B.
(2)Lay down viewing steps from the mountaintop down to the hill along the hillside line. For these steps, the height of each step is 20 centimeters, the length is due to the slope, but the length couldn’t less than 20 centimeters. Two endpoints of each step are on the hill slope (as the graph shown).
①Calculate the length of the first three steps respectively. (Accurate to centimeters)
②why does this step can't been spread to the bottom of the hill?
(3) There is a small piece of ground on point D which is 700 meters high from the foot of the hill, and this ground can be used to build a cableway station. The starting point of the cableway is set at point E which is at the bottom level of the hill, and m. Assume that cableway DE is approximately considered as a parabolic which has the point E as the vertex and opens up, and its analysis formula is . Try to search the maximum dangling height of the cableway.
This is a practical problem in the construction which involves laying down viewing steps and building a cableway station. The key to solve this problem is to express this problem in the form of a quadratic function. Here are the solutions to these questions.
(1) is an arbitrary point on the l
