二次函数图像分析范例 by Walch Education

GeoGebra 命令及参数

1. If(abs(a) ≟ 1, If[a ≟ 1, ha, (-ha(x))], h) → h1
2. Factors(h) → factorsh
3. If(abs(a) ≟ 1, If[a ≟ 1, "", "-"], LaTeX[a]) → a1
4. If(abs(a_1) ≟ 1, If[a_1 ≟ 1, ha_1, (-ha_1(x))], h_1) → h1_1
5. Factors(h_1) → factorsh_1
6. Polygon((edge, y(Corner[1])), Corner[2], Corner[3], (edge, y(Corner[4]))) → Mask, b, c, d, e
7. TableText({{"\textit{f}(\textit{x})=" + (LaTeX[h1]), "\text{Original equation}"}, {" 0=" + (LaTeX[h1]), "\text{Set the equation equal to 0}."}, {" 0=" + (LaTeX[factor1]) + "\text{ or }0=" + (LaTeX[factor2]), "\text{Set each factor equal to 0.}"}, {"\textcolor{Brown}{" + (LaTeX[root1]) + "}=x\text{ or }\textcolor{Brown}{" + (LaTeX[root2]) + "}=x", "\text{Solve each equation for }\textit{x}. "}}, "l") → Conclusion1
8. TableText({{"\textit{f}(\textit{x})=" + (LaTeX[h1]), "\text{Original equation}"}, {"\textit{f}(" + (LaTeX[rootav]) + ")=" + (LaTeX[a1]) + "(" + (LaTeX[rootav]) + "" + (LaTeX[Element[plus, sgn((-root1)) + 2]]) + "" + (LaTeX[(-root1)]) + ") (" + (LaTeX[rootav]) + " " + (LaTeX[Element[plus, sgn((-root2)) + 2]]) + "" + (LaTeX[(-root2)]) + ")", "\text{Substitute }\textcolor{magenta}{ " + (LaTeX[rootav]) + "}\text{ for }\textit{x}."}, {"\textit{f}(" + (LaTeX[rootav]) + ")=" + (LaTeX[a1]) + "(" + (LaTeX[factor1(rootav)]) + ")(" + (LaTeX[factor2(rootav)]) + ")", "\text{Simplify.}"}}, "l") → Conclusion3b