quadratic curve

简明释义

二次曲线

英英释义

例句

1.When analyzing the data, we noticed that it followed a quadratic curve 二次曲线, indicating a parabolic trend.

在分析数据时，我们注意到它遵循了一条quadratic curve 二次曲线，表明呈现出抛物线趋势。

2.The path of the projectile can be modeled by a quadratic curve 二次曲线 that describes its motion.

抛射物的轨迹可以用一个quadratic curve 二次曲线来建模，描述其运动。

3.A quadratic curve 二次曲线 can be represented by the equation y = ax² + bx + c.

一条quadratic curve 二次曲线可以用方程y = ax² + bx + c表示。

4.In algebra, we often graph a quadratic curve 二次曲线 to find the roots of a quadratic equation.

在代数中，我们常常绘制quadratic curve 二次曲线来寻找二次方程的根。

5.The design of the arch was based on a quadratic curve 二次曲线, which provides both strength and aesthetic appeal.

拱门的设计基于一条quadratic curve 二次曲线，既提供了强度又具有美观性。

作文

Mathematics is a fascinating subject that plays a crucial role in our daily lives. One of the fundamental concepts in mathematics is the idea of curves, particularly the quadratic curve, which is defined by a polynomial equation of degree two. Understanding quadratic curves is essential for various applications in fields such as physics, engineering, and economics.A quadratic curve can be represented by the equation y = ax² + bx + c, where 'a', 'b', and 'c' are constants, and 'x' is the variable. The shape of this curve is a parabola, which can either open upwards or downwards depending on the sign of 'a'. If 'a' is positive, the parabola opens upwards, creating a U-shape that has a minimum point known as the vertex. Conversely, if 'a' is negative, the parabola opens downwards, forming an inverted U-shape with a maximum point at the vertex.The vertex of a quadratic curve is a significant feature because it indicates the highest or lowest point on the curve, depending on its orientation. The coordinates of the vertex can be calculated using the formula (-b/2a, f(-b/2a)), where 'f' represents the function defined by the quadratic curve. This vertex not only helps in graphing the curve but also provides insights into the behavior of the function it represents.Another important aspect of quadratic curves is their symmetry. A quadratic curve is symmetric about a vertical line known as the axis of symmetry, which can be found at x = -b/2a. This property makes it easier to sketch the graph of a quadratic curve since one can plot points on one side of the axis and reflect them over to the other side.In real-world scenarios, quadratic curves often model various phenomena. For instance, the trajectory of a projectile can be described by a quadratic curve. When an object is thrown into the air, its height over time forms a parabolic shape due to the influence of gravity. This understanding allows engineers to calculate the optimal angle for launching projectiles to achieve maximum distance.Moreover, quadratic curves are widely used in economics to represent cost and revenue functions. Businesses often encounter situations where they need to determine the maximum profit or minimum cost. By analyzing the quadratic curve derived from their cost and revenue equations, they can identify the optimal production levels that yield the best financial outcomes.In conclusion, the study of quadratic curves is not just an abstract mathematical concept; it has practical implications across various fields. From physics to economics, understanding how to manipulate and interpret quadratic curves can provide valuable insights and solutions to real-world problems. As we continue to explore the world of mathematics, the significance of quadratic curves will undoubtedly remain prominent, helping us to better understand the complexities of the universe around us.

数学是一个迷人的学科，在我们的日常生活中发挥着至关重要的作用。数学中的一个基本概念是曲线的概念，特别是二次曲线，它由二次多项式方程定义。理解二次曲线对于物理、工程和经济等领域的各种应用至关重要。二次曲线可以用方程y = ax² + bx + c表示，其中'a'、'b'和'c'是常数，而'x'是变量。该曲线的形状是抛物线，取决于'a'的符号，它可以向上或向下打开。如果'a'为正，则抛物线向上打开，形成一个U形，具有一个称为顶点的最小点。相反，如果'a'为负，则抛物线向下打开，形成一个倒U形，其顶点处有一个最大点。二次曲线的顶点是一个重要特征，因为它指示曲线上的最高或最低点，具体取决于其方向。顶点的坐标可以使用公式(-b/2a, f(-b/2a))计算，其中'f'表示由二次曲线定义的函数。这个顶点不仅有助于绘制曲线，还提供了对其所代表的函数行为的深入理解。二次曲线的另一个重要方面是它们的对称性。二次曲线关于一条称为对称轴的垂直线对称，该对称轴可以在x = -b/2a处找到。这一特性使得绘制二次曲线的图形变得更加容易，因为人们可以在对称轴的一侧绘制点，然后在另一侧进行反射。在现实世界的场景中，二次曲线通常用于建模各种现象。例如，投射物的轨迹可以用二次曲线来描述。当一个物体被抛向空中时，其高度随时间的变化形成一个抛物线形状，这是由于重力的影响。这种理解使工程师能够计算出投射物的最佳发射角度，以达到最大距离。此外，二次曲线在经济学中被广泛用于表示成本和收益函数。企业经常遇到需要确定最大利润或最低成本的情况。通过分析从其成本和收益方程推导出的二次曲线，他们可以识别出产生最佳财务结果的最佳生产水平。总之，研究二次曲线不仅仅是一个抽象的数学概念；它在各个领域都有实际的意义。从物理到经济学，理解如何操作和解释二次曲线可以提供有价值的见解和解决现实问题的方案。随着我们继续探索数学的世界，二次曲线的重要性无疑将保持突出，帮助我们更好地理解周围宇宙的复杂性。