二次方程

世界充滿著未知，人類以智慧的鑰匙開啟了科學大廈中無數從未知通向已知的大門，無數中外先輩的閃光思想和超前智慧同樣地凝結在二次方程的研究中。人類歷經了2 000多年的努力，才將二次方程的解法與理論基礎徹底搞清楚。在今天的生活里，二次方程起到的作用是不容忽視的。

In reality the quadratic equation as many functions in the scientific and mathematical world. The equation is used to find shapes， circles， ellipses， parabolas， and more. The quadratic equation looks a little menacing， however it is not .

we will be discussing the quadratic equation. It is primarily used to find the curve that objects take when they fly through the air. For example a softball， tennis ball， football， baseball， soccer ball， basketball， etc. It also used to design any object that has curves and any specific curved shape needed for a project. The military uses the quadratic equation when they want to predict where artillery shells hit the earth or target when fired from cannons.

Other uses of the quadratic equation include explaining how planets in our solar system revolve around the sun. Our planets were initially tracked by early scientists， who did not have the advantage of computers， and they used the quadratic equation to determine how planets in our solar system do not have circular orbits - they have elliptical orbits.

The quadratic equation is used by car makers to determine how much and what type of brakes are needed to stop a car going at various speeds. This and other design functions which use the quadratic equation are part of the design steps of a new car， truck， motorcycle， and other types of automobiles.

When a police officer investigates a car accident scene， he/she uses the quadratic equation in their efforts to determine what velocities the cars when traveling when the collision occurred. Also， who was at fault and why the vehicles were damaged the way they were. These calculations are also used by car designers to develop an even safer care for occupants during future collisions.

The quadratic equation has many practical applications in the world beyond school. You may not think you need to know it now; however the higher paying jobs go to those who can use the quadratic equation to design safe and useful products for people.

現實生活中的二次方程在科學與數學領域中有著許多功能，例如通過二次方程式來求圓、橢圓、拋物線等。二次方程看起來很難，但其實并非如此。

今天我們要來討論一下二次方程。二次方程起初用來表示物體從空中滑落時的曲線，例如壘球、網球、足球、棒球、橄欖球、籃球等。它也用于工程中設計任何曲面或者具有特殊曲面形狀的物體。在軍事上，人們用二次方程來預測大炮開火時，子彈將在哪里落下或擊中目標。

二次方程還可以解釋行星如何圍繞太陽運動。早期的科學家對行星進行的研究分析就是通過二次方程來進行的，因為那時還沒有電腦。科學家還通過二次方程發現行星圍繞太陽運行的軌道不是圓形，而是橢圓形。

汽車制造者通過二次方程來決定不同速度的剎車的價格和類型。在小轎車，大卡車，摩托車和其他機動車輛的設計過程中，二次方程在剎車和許多部件的設計方面都發揮了作用。

警察在車禍現場進行調查時，用二次方程來計算車輛相撞時的速率，并斷定哪一方需承擔責任以及他們的車輛毀壞的原因。這一系列的計算也為汽車設計師提供了數據，使他們在設計中最大程度地提高駕駛者的安全系數。

二次方程在校園之外的現實生活中有很多切合實際的應用，也許你現在并不想去掌握它，不過值得提醒一下的是，高薪的工作是屬于那些熟練掌握二次方程，并以此為人們設計出更安全、實用產品的人哦！

實戰演練

1. If f （x）＝ax4-bx2＋x＋5 and f（-3）＝2， then what is f（3）?

2. For what real values of x is （1-｜x｜）（1＋x） positive?

3. A rubber ball is dropped from a 100 ft tall building. Each time it bounces， it rises to three－quarters its previous height. So， after its first bounce it rises to 75 ft， and after its second bounce it rises toof 75 ft， and so on forever. What is the total distance the ball travels?

4. The principal of a new elementary school sounded the alarm for fire training. It took a very long time to empty the building. It was evident that the school children were at risk. The school has three exterior doors. The main door is served by a wide corridor， the side door by a narrower corridor， and the rear door by a dog－legged corridor. By experimenting with the classrooms adjacent to each of these doors， it was determined that: About 1.5 minutes elapse between the announcement of an emergency and the first departure through each door. Students and staff can file through the doors at these rates approximately 55 per minute through the main door， 30 per minute through the side door， and 25 per minute through the rear door. About 450 persons are inside the building. Calculate for the problem the minimum time until the building empties

A. 4.1B. 1.5

C. 5.3D. 5.6

E. 8.18

5. If x is a positive integer satisfying x7=k and x9=m， which of the following must be equal to x11?

A. B. m2-k

C. m2-7D. 2k-

E. k+4

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1. Oranges weigh 1 unit， apples weigh 5 units， and bananas weigh 2 units.

2. x4-x3y+x2y2-xy3+y4x5+y5

3. －1

4. ，1，－1，and－

5. The radius is 6 and the center is （－2，2）