⬛ 配方法计算器Completing the Square Calculator
把二次式 ax² + bx + c 配方为顶点式 a(x − h)² + k，列出配方步骤，并给出顶点、对称轴和方程 ax² + bx + c = 0 的解（含复数根）。Rewrite ax² + bx + c in vertex form a(x − h)² + k by completing the square, with the steps, the vertex, the axis of symmetry and the solutions of ax² + bx + c = 0, including complex roots.
使用说明与常见问题How-to & FAQ
「配方法计算器」是什么？What is the Completing the Square Calculator tool?
把二次式 ax² + bx + c 配方为顶点式 a(x − h)² + k，列出配方步骤，并给出顶点、对称轴和方程 ax² + bx + c = 0 的解（含复数根）。Rewrite ax² + bx + c in vertex form a(x − h)² + k by completing the square, with the steps, the vertex, the axis of symmetry and the solutions of ax² + bx + c = 0, including complex roots.
如何使用「配方法计算器」？How do I use the Completing the Square Calculator tool?
在「配方法计算器」中，填写「a」、「b」、「c」等参数，结果会随输入实时计算并显示在下方。In the Completing the Square Calculator: Fill in "a", "b", "c"; results are recalculated instantly as you type.
配方法的步骤？What are the steps?
1）提出 a；2）括号内加上并减去 (b/2a)²；3）把前三项写成完全平方，得到 a(x − h)² + k，其中 h = −b/(2a)，k = c − b²/(4a)。1) Factor out a; 2) inside the bracket add and subtract (b/2a)²; 3) write the first three terms as a perfect square to get a(x − h)² + k, with h = −b/(2a) and k = c − b²/(4a).
顶点式有什么用？Why use vertex form?
顶点式直接给出抛物线的顶点 (h, k) 和对称轴 x = h，也能直接解出 x = h ± √(−k/a)。Vertex form shows the parabola's vertex (h, k) and axis x = h at a glance, and solves directly as x = h ± √(−k/a).
计算精度如何？How precise are the results?
「配方法计算器」使用 JavaScript 双精度浮点数（约 15–16 位有效数字）；极大或极小的数值可能存在精度误差。The Completing the Square Calculator uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「配方法计算器」免费吗？需要注册吗？Is the Completing the Square Calculator free? Do I need an account?
「配方法计算器」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Completing the Square Calculator is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.