quadratics

简明释义

英[kwɒˈdrætɪks]美[kwɑːˈdrætɪks]

n. 二次方程式论（quadratic 的复数形式）

英英释义

单词用法

同义词

反义词

例句

1.The engineer used quadratics 二次方程 to model the trajectory of the projectile.

工程师使用quadratics 二次方程来建模抛射物的轨迹。

2.Many real-world problems can be represented by quadratics 二次方程.

许多现实世界的问题可以用quadratics 二次方程表示。

3.The graph of a quadratic 二次方程 function is a parabola.

一个quadratic 二次方程函数的图形是一个抛物线。

4.Understanding quadratics 二次方程 is essential for advanced mathematics courses.

理解quadratics 二次方程对高级数学课程至关重要。

5.In algebra class, we learned how to solve quadratics 二次方程 using the quadratic formula.

在代数课上，我们学习了如何使用二次公式解决quadratics 二次方程。

作文

Quadratics, or 二次方程, are a fundamental concept in algebra that deal with polynomial equations of degree two. The general form of a quadratic equation is expressed as ax² + bx + c = 0, where a, b, and c are constants, and x represents the variable. Understanding 二次方程 is crucial not only for academic purposes but also for real-world applications. These equations can model various phenomena, such as the trajectory of an object in motion or the shape of a parabolic structure.One of the most significant aspects of 二次方程 is the quadratic formula, which provides a method for finding the roots of these equations. The formula is given by x = (-b ± √(b² - 4ac)) / (2a). This formula allows us to determine the values of x that satisfy the equation, which is essential for solving problems in physics, engineering, and economics. The discriminant, represented by D = b² - 4ac, plays a vital role in determining the nature of the roots. If D > 0, the quadratic has two distinct real roots; if D = 0, there is exactly one real root; and if D < 0, the roots are complex numbers.In addition to the quadratic formula, 二次方程 can be solved by factoring, completing the square, or graphing. Each method has its advantages depending on the context of the problem. For example, factoring is often the quickest method when the equation can be expressed as a product of two binomials. Completing the square is particularly useful when deriving the vertex form of a quadratic function, which reveals important information about its graph.The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the leading coefficient (a). The vertex of the parabola represents the maximum or minimum point of the function, and the axis of symmetry is a vertical line that passes through this vertex. Understanding the graphical representation of 二次方程 helps in visualizing the solutions and the behavior of the function.Moreover, 二次方程 are widely used in various fields such as physics, finance, and biology. For instance, in physics, they can describe the motion of projectiles, where the height of an object can be modeled using a quadratic function of time. In finance, quadratic equations are used in calculating profit maximization and loss minimization scenarios. In biology, they can help model population growth under certain conditions.In conclusion, mastering 二次方程 is essential for students and professionals alike. Not only do they serve as a stepping stone for more advanced mathematical concepts, but they also have practical applications across numerous disciplines. By understanding the properties, methods of solving, and real-world implications of 二次方程, individuals can enhance their analytical skills and improve their ability to tackle complex problems. As we continue to explore the world around us, the relevance of 二次方程 will undoubtedly remain significant, reinforcing the importance of this topic in our educational journey.