📚 Quadratic Equations: Factorisation, Formula and Graphs | 二次方程：因式分解、公式与图像
Quadratic equations appear throughout the IGCSE Mathematics syllabus, from algebra and graphs to real-world problems involving area, motion and profit. Understanding how to recognise, solve and sketch quadratics is essential for success in both core and extended papers.
二次方程贯穿 IGCSE 数学大纲，从代数、图像到涉及面积、运动与利润的实际问题。掌握二次方程的识别、求解与图像绘制，对核心卷和扩展卷的考试成功都至关重要。
1. Introduction to Quadratic Equations | 二次方程简介
tants and a ≠ 0. The highest power of the unknown x is 2, which gives the graph its characteristic U-shape called a parabola.
二次方程是任何可以写成一般形式 ax² + bx + c = 0 的方程，其中 a、b、c 为常数且 a ≠ 0。未知数 x 的最高次数为 2，这使得它的图像呈现特有的 U 形，称为抛物线。
ic. For example, 2x² - 3x + 1 = 0 is quadratic, but 0x² + 5x - 7 = 0 is simply 5x - 7 = 0.
如果 a = 0，方程就变成一次方程而不是二次方程。例如，2x² - 3x + 1 = 0 是二次方程，而 0x² + 5x - 7 = 0 其实就是 5x - 7 = 0。
2. Standard Form and Key Terms | 标准形式与关键术语
, b and c. For example, in the equation 3x² - 6x + 2 = 0, we have a = 3, b = -6 and c = 2.
求解之前，一定要把方程整理成标准形式 ax² + bx + c = 0。这样可以更容易识别系数 a、b 和 c。例如，在方程 3x² - 6x + 2 = 0 中，系数为 a = 3、b = -6、c = 2。
giving a = 4, b = -2 and c = -5. Missing terms mean the corresponding coefficient is zero.
有些方程需要先移项。例如，4x² = 2x + 5 应写成 4x² - 2x - 5 = 0，因此 a = 4、b = -2、c = -5。缺少某一项意味着对应系数为 0。
Key terms include the roots or solutions, which are the x-values that make the equation true
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