抛物线方程书写练习

几何画板及绘图内容加载中，请稍等……

2026-02-18 22:30

函数解析几何函数图像

所属专题 Coordinate Geometry

本范例是一个交互式数学练习，引导学生求解形如 y = ax² + bx + c 的抛物线方程并检验理解。核心数学概念包括二次函数、抛物线图像特征、方程系数与图像关系（开口方向、顶点位置、与坐标轴交点）。构造要点：利用 GeoGebra 的 Coefficients 命令提取多项式系数，通过 Random 和 Shuffle 命令随机生成练习题目，采用 Textfield 和 InputBox 组件构建输入界面，配合 btnValidate 按钮实现答案验证功能，并设置 showanswer、showsolution 等对象展示正确答案与解题步骤。适合中学数学课程中二次函数单元的课堂练习或课后巩固，可帮助学生掌握从图像信息反推函数解析式的能力。

GeoGebra 命令及参数

Shuffle({1, 2, 3, 4, 5, 6, 7}) → allCaseNum, {2, 7, 3, 6, 5, 1, 4}
Element(allCaseNum, Mod[countQuestion, Length[allCaseNum]] + 1) → caseNum
Random(-5, 5) → ascV
Random(-6, 6) → ordV
Random(-6, 6) → intY
Random(-6, 6) → intX
Random(-5, 5) → as
Shuffle(Join[Sequence[Sequence[(j, k), j, -10, 10, 1], k, -10, 10, 1]]) → bigGrid, {(0, 3), (-5, -10), (-7, 3), (-9, 5), (6, -4), (-3, -5), (0, 7), (-7, -4), (0, -5), (-1, -4), (-2, 6), (8, 6), (-9, -7), (-9, 4), (8, -1), (-3, 7), (-10, 3), (7, -10), (-8, 5), (-4, -8), (6, -7), (4, -3), (1, -4), (-1, 0), (-4, -7), (2, 8), (10, -8), (1, 0), (-7, 7), (8, -7), (-9, -2), (8, 8), (7, 8), (-7, 1), (2, -7), (-4, 4), (2, 0), (3, -4), (1, 9), (-10, 7), (5, -7), (-1, 7), (3, -8), (-4, -4), (-1, 9), (-1, -9), (-1, 3), (4, -6), (-6, 1), (-3, 6), (-4, -9), (-1, 1), (0, -6), (-7, -1), (7, -5), (-2, 2), (-2, -1), (5, 1), (-7, -3), (9, -1), (-9, -6), (3, -5), (-7, -7), (-8, 6), (5, -3), (8, 2), (-9, -10), (2, -4), (5, 7), (1, 7), (4, -1), (-7, 8), (5, 10), (-8, 3), (-3, 10), (-5, -4), (6, -2), (-7, 10), (1, -8), (5, 5), (8, 5), (7, 6), (-2, 7), (-5, 10), (6, -8), (-3, -9), (7, 9), (-5, -3), (2, -9), (3, 4), (4, -8), (-3, 5), (-10, -7), (-4, 7), (-10, -10), (0, -1), (4, 2), (0, 4), (-9, 0), (0, -2), (6, -9), (0, -9), (10, 3), (9, -8), (-5, 8), (-4, 5), (9, -2), (-6, 7), (-10, 9), (-10, 2), (2, 7), (-4, 8), (10, 4), (8, -10), (10, -1), (7, 7), (7, -4), (-10, -1), (-10, 8), (6, 1), (10, 5), (2, 6), (10, -3), (-3, -3), (2, -6), (10, -4), (4, 4), (6, 7), (5, -2), (3, -10), (1, 1), (-6, 9), (-4, 10), (2, 10), (-1, -8), (2, 2), (9, -4), (-2, -5), (1, -2), (-4, -2), (8, -6), (-7, -2), (1, 4), (-7, -9), (3, 2), (1, 3), (5, 8), (6, 3), (7, -9), (-8, 8), (-10, -2), (-6, 3), (-5, 4), (8, 1), (-10, 0), (-10, -9), (-1, -7), (-1, 6), (-2, 5), (-4, 0), (0, 10), (-9, -9), (2, -1), (-6, -5), (4, -4), (1, 5), (1, 8), (-4, 3), (-3, 1), (8, -4), (-1, -5), (-2, -10), (-8, -6), (10, -5), (1, -10), (-10, 4), (6, 4), (-3, 0), (-9, -8), (6, 0), (1, -6), (4, 3), (3, -9), (-4, 6), (3, 8), (4, -9), (-5, -6), (4, -2), (-2, -2), (5, -8), (-8, 1), (4, 0), (-9, -3), (-3, -10), (4, 1), (-7, -8), (3, 5), (-9, 7), (10, 6), (-1, -1), (4, 8), (1, -5), (2, 5), (-5, -2), (-7, -10), (-6, -7), (4, 7), (10, 7), (6, -10), (6, 9), (-10, -4), (-6, 6), (7, 0), (7, -7), (-2, -8), (9, 2), (-7, 9), (-4, -10), (6, 5), (0, -8), (-1, 4), (-9, 6), (-3, -8), (-1, 2), (-6, -6), (-2, 9), (-6, -2), (8, -8), (3, -6), (9, 10), (2, -3), (0, 6), (9, 1), (-8, -9), (10, -9), (7, -3), (-5, -5), (-9, -1), (-4, 2), (0, 5), (7, -6), (-6, 8), (-1, -10), (-9, -4), (5, 3), (5, -9), (-5, -7), (5, -10), (-5, 6), (9, -3), (2, -8), (0, 2), (10, -7), (0, 1), (9, 9), (6, 2), (-8, 7), (-5, 1), (4, -7), (-2, -4), (-3, -6), (-6, 10), (6, -3), (-5, 9), (-9, 10), (-2, -9), (-8, 2), (8, 3), (3, 6), (8, -5), (2, -5), (5, -6), (5, 0), (6, 8), (-5, 5), (5, -1), (6, -1), (0, 9), (-2, -6), (-1, -6), (-4, -6), (-6, -8), (-2, 0), (10, 8), (1, -3), (5, 4), (-10, 10), (4, 9), (0, -3), (7, 10), (4, -5), (-10, -6), (5, 6), (9, 6), (6, -6), (9, 3), (10, 2), (4, 10), (-5, -8), (-2, 8), (-6, -4), (2, 4), (8, -3), (5, -5), (10, -6), (10, 9), (-9, 1), (3, 9), (10, -10), (-9, 8), (-8, -7), (1, 6), (-1, 5), (-3, -1), (-9, -5), (2, 3), (-10, 5), (1, -1), (8, 9), (3, 1), (-2, -7), (5, -4), (-3, -7), (-7, 4), (-10, 1), (7, -8), (9, -5), (9, -7), (-8, -10), (9, -10), (-10, -3), (-2, 3), (7, 1), (-7, -5), (-6, 2), (-3, -2), (-4, -3), (1, -9), (2, -10), (3, -1), (6, 6), (-4, 9), (-6, -10), (-8, 9), (-1, 10), (1, 10), (-10, 6), (-3, 4), (5, 2), (-8, -2), (9, -6), (-10, -5), (-6, 4), (1, -7), (-9, 2), (-2, 10), (-2, 4), (0, -10), (8, 0), (-4, -5), (-3, -4), (9, 0), (-1, -3), (-8, -3), (-3, 2), (6, -5), (-7, 0), (7, -1), (0, -7), (-6, -1), (-1, 8), (3, 0), (0, 8), (5, 9), (6, 10), (10, -2), (-7, 5), (10, 0), (0, -4), (8, -2), (-8, 4), (3, -3), (-5, -9), (0, 0), (-4, 1), (2, -2), (-7, 6), (10, 1), (9, 4), (7, 4), (-5, 0), (-8, -4), (-3, 8), (-8, -8), (3, 3), (8, 10), (2, 1), (3, -2), (9, -9), (1, 2), (3, 7), (-10, -8), (-9, 9), (10, 10), (-3, 3), (-7, 2), (-8, -5), (8, -9), (8, 7), (-6, 0), (-8, 0), (-8, -1), (-5, 2), (8, 4), (-5, 3), (7, 5), (3, 10), (4, 5), (-7, -6), (-2, 1), (4, -10), (9, 8), (-1, -2), (9, 7), (9, 5), (-9, 3), (-5, 7), (-6, 5), (-3, 9), (7, -2), (-8, 10), (-4, -1), (3, -7), (7, 3), (-6, -9), (4, 6), (7, 2), (-2, -3), (-6, -3), (2, 9), (-5, -1)}
Element(bigGrid, Mod[countQuestion, Length[bigGrid]] + 1) → V1
Coefficients(inputA) → allCoeff
Textfield(inputB) → InputBoxB
Corner(5) → layoutAppSize
onboardingTextOffset(Corner[onboardingText, 1], Corner[onboardingText, 3], onboardingCase, Corner[1], Corner[3], Corner[5]) → OnboardingTextOffset
Textfield(inputA) → InputBoxA
Textfield(inputC) → InputBoxC
Polygon(P1, Mirror[P1, yAxis], Mirror[P1, (0, 0)], Mirror[P1, xAxis]) → peep, f, g, h, i
Segment((-10.8, 0), (10.8, 0)) → fakeX
Segment((0, -10.8), (0, 10.8)) → fakeY
Vector(V1, (0, 0)) → aniVec
Vector((10, 0), (11.2, 0)) → arrowX
Vector((0, 10), (0, 11.2)) → arrowy

AI 绘图提示语参考

绘制一个开口向上的抛物线，给定顶点坐标为(-3, 4)，并随机生成一个过该顶点的抛物线方程。首先，画出坐标轴，然后在坐标系中随机生成一个顶点，接着根据顶点坐标和随机生成的参数绘制抛物线，最后在坐标系中随机显示一个点，并要求用户根据该点的坐标推导出抛物线的方程。

以上提示语为根据原始绘图命令整理而来，仅供参考。