配方法入门
几何画板及绘图内容加载中,请稍等……
①本范例演示通过图形变换演示配方法将二次函数转化为顶点式;②涉及核心数学概念:二次函数、配方法、顶点式、几何变换;③作图要点:使用Segment, Polygon, Sequence, Point, Dilate, Rotate, Vector, Translate, Distance, Textfield等命令和对象构建图形;④适合初中及以上学生学习和理解二次函数性质及配方法应用。
GeoGebra 命令及参数
Segment(A, B) → fSegment(D, C) → hSegment(C, A) → iPolygon(A, B, D, C) → poly1, a_1, b_1, d, cSequence((a + i, 0), i, 0, abs(b / 2), 1) → bottomsSequence((a + i, a), i, 0, abs(b / 2), 1) → topsSequence((0, a + i), i, 0, abs(b / 2), 1) → leftsSequence((a, a + i), i, 0, abs(b / 2), 1) → rightsSequence(Dilate[Element[bottoms, i], If[0 < g ≤ 1, 1 - g, 0], Element[tops, i]], i, 0, abs(b / 2) + 1, 1) → bottomsmoveSequence(Dilate[Element[lefts, i], If[1 < g ≤ 2, 2 - g, 0], Element[rights, i]], i, 0, abs(b / 2) + 1, 1) → leftsmovePoint(bottomsmove) → ESegment(B, E) → jDilate(C, If[1 < g ≤ 2, 2 - g, 0], D) → C'Segment(C, C') → kPolygon(D, H, F, G) → poly2, d_1, h_1, f_1, g_1Dilate(H, If[2 < g ≤ 3, 3 - g, 0], F) → H'Dilate(G, If[2 < g ≤ 3, 3 - g, 0], F) → G'Dilate(I, If[2 < g ≤ 3, 3 - g, 0], A) → I'Segment(I, I') → lRotate(I, If[3 < g ≤ 4, ((-(g - 3)) * π / 2), ((-π)) / 2], A) → I'_1Rotate(I', If[3 < g ≤ 4, ((-(g - 3)) * π / 2), ((-π)) / 2], A) → I''Segment(I'_1, I'') → l'Rotate(I'_1, If[4 < g ≤ 5, ((-(g - 4)) * π / 2), ((-π)) / 2], I'_1) → JRotate(I'', If[4 < g ≤ 5, ((-(g - 4)) * π / 2), ((-π)) / 2], I'_1) → I'''Segment(J, I''') → l''Dilate(A, If[5 < g ≤ 6, 6 - g, 0], I) → A'Vector(A, A') → uTranslate(I'_1, u) → KTranslate(I'', u) → I'''_1Segment(K, I'''_1) → l''_1Sequence(Segment[Element[bottoms, i + 1], Element[bottomsmove, i + 2]], i, 1, abs(b / 2), 1) → list1Sequence(Segment[Element[lefts, i + 1], Element[leftsmove, i + 2]], i, 1, abs(b / 2), 1) → list2Sequence(Polygon[Element[bottoms, i], Element[bottoms, i + 1], Element[tops, i + 1], Element[tops, i]], i, 1, abs(b / 2), 1) → list3Sequence(Polygon[Element[lefts, i], Element[lefts, i + 1], Element[rights, i + 1], Element[rights, i]], i, 1, abs(b / 2), 1) → list4Distance(D, F) → distanceDFTextfield(b) → InputBox1
AI 绘图提示语参考
画一个演示二次函数配方法的图形,展示几何变换将二次函数转换为顶点形式。首先画出一条基线段,然后通过几何变换(如缩放、旋转和平移)构建一系列多边形,最终形成顶点形式。用不同颜色或线条样式区分原始图形和变换后的图形,并标注关键点和变换过程,帮助理解二次函数的性质和配方法的应用。
以上提示语为根据原始绘图命令整理而来,仅供参考。