⌒ 抛物线计算器Parabola Calculator
由一般式 y = ax² + bx + c 或顶点式 y = a(x − h)² + k 求抛物线的顶点、焦点、准线、对称轴、开口方向、焦距、通径长度以及与坐标轴的交点。From y = ax² + bx + c or the vertex form y = a(x − h)² + k, find a parabola's vertex, focus, directrix, axis of symmetry, direction, focal length, latus rectum and axis intercepts.
使用说明与常见问题How-to & FAQ
「抛物线计算器」是什么？What is the Parabola Calculator tool?
由一般式 y = ax² + bx + c 或顶点式 y = a(x − h)² + k 求抛物线的顶点、焦点、准线、对称轴、开口方向、焦距、通径长度以及与坐标轴的交点。From y = ax² + bx + c or the vertex form y = a(x − h)² + k, find a parabola's vertex, focus, directrix, axis of symmetry, direction, focal length, latus rectum and axis intercepts.
如何使用「抛物线计算器」？How do I use the Parabola Calculator tool?
在「抛物线计算器」中，填写「形式」、「a」、「b」、「c」、「h」等参数，结果会随输入实时计算并显示在下方。In the Parabola Calculator: Fill in "Form", "a", "b", "c", "h"; results are recalculated instantly as you type.
焦点和准线怎么求？How are the focus and directrix found?
把方程化为顶点式 y = a(x − h)² + k，焦距 p = 1/(4a)，焦点为 (h, k + p)，准线为 y = k − p。抛物线上每一点到焦点和到准线的距离相等。Write it as y = a(x − h)² + k; with p = 1/(4a) the focus is (h, k + p) and the directrix is y = k − p. Every point on the parabola is equally far from both.
结果为什么是分数？Why are results shown as fractions?
能化成分母不超过 10,000 的分数时用分数显示，更便于核对作业；否则显示小数。Values that are fractions with a denominator up to 10,000 are shown exactly, which makes homework easier to check; otherwise decimals are shown.
计算精度如何？How precise are the results?
「抛物线计算器」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 Parabola Calculator uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「抛物线计算器」免费吗？需要注册吗？Is the Parabola Calculator free? Do I need an account?
「抛物线计算器」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 Parabola 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.