求具有最小值点的二次函数方程

GeoGebra 命令及参数

1. If(x(B) ≟ x(A), B + (1, 0), B) → V
2. Polygon((edge, y(Corner[1])), Corner[2], Corner[3], (edge, y(Corner[4]))) → Mask, mask1, mask2, mask4, mask3
3. If(abs(b) ≟ 1, If[b ≟ 1, "", "-"], LaTeX[b]) → b1
4. If(abs(c) ≟ 1, If[c ≟ 1, "", "-"], LaTeX[c]) → c1
5. TableText({{"\textit{f}(\textit{x})=\textit{a}(\textit{x} " + (LaTeX[Element[plus, sgn((-x(V))) + 2]]) + "" + (LaTeX[(-x(V))]) + " )^2" + (LaTeX[Element[plus, sgn(y(V)) + 2]]) + "" + (LaTeX[y(V)]), " \text{Equation from step 1.}"}, {" \textit{f}(\textit{x})= \frac{" + (LaTeX[y(A) - y(V)]) + "}{" + ((LaTeX[x(A)^(2)] * "}(\textit{x} ")) + (LaTeX[Element[plus, sgn((-x(V))) + 2]]) + "" + (LaTeX[(-x(V))]) + " )^2 " + (LaTeX[Element[plus, sgn(y(V)) + 2]]) + "" + (LaTeX[y(V)]), " "}}, "l") → Conclusions3
6. TableText({{"\textit{f}(\textit{x})= \textit{a}(\textit{x}-\textit{h})^2+\textit{k}", " \text{Vertex form}"}, {" \textit{f}(\textit{x})=\textit{a}[\textit{x}-(" + (LaTeX[x(V)]) + ")]^2+(" + (LaTeX[y(V)]) + ") ", "\text{Substitute " + (LaTeX[V]) + " for } \textit{h}\text{ and }\textit{k}."}, {" \textit{f}(\textit{x})=\textit{a} (\textit{x}" + (LaTeX[Element[plus, sgn((-x(V))) + 2]]) + "" + (LaTeX[(-x(V))]) + ")^2" + (LaTeX[Element[plus, sgn(y(V)) + 2]]) + "" + (LaTeX[y(V)]), "\text{Simplify.}"}}, "l") → Conclusions1
7. TableText({{"\textit{f}(\textit{x})=\textit{a}(\textit{x}" + (LaTeX[Element[plus, sgn((-x(V))) + 2]]) + " " + (LaTeX[(-x(V))]) + ")^2 " + (LaTeX[Element[plus, sgn(y(V)) + 2]]) + " " + (LaTeX[y(V)]), "\text{Equation from step 1.} "}, {LaTeX[y(A)] + "=\textit{a}[(" + (LaTeX[x(A)]) + ")" + (LaTeX[Element[plus, sgn((-x(V))) + 2]]) + " " + (LaTeX[(-x(V))]) + "]^2" + (LaTeX[Element[plus, sgn(y(V)) + 2]]) + " " + (LaTeX[y(V)]), "\text{Substitute }" + (LaTeX[A]) + "\text{ for } \textit{x} \text{ and }\textit{f}(\textit{x}). "}, {LaTeX[y(A)] + "=a[" + (LaTeX[x(A)]) + "]^2" + (LaTeX[Element[plus, sgn(y(V)) + 2]]) + "" + (LaTeX[y(V)]), "\text{Simplify.}"}, {LaTeX[y(A)] + "=" + (LaTeX[x(A)^(2)]) + "\textit{a}" + (LaTeX[Element[plus, sgn(y(V)) + 2]]) + "" + (LaTeX[y(V)])}, {LaTeX[y(A) - y(V)] + "=" + (LaTeX[x(A)^(2)]) + "\textit{a}", " "}, {" \frac{" + (LaTeX[y(A) - y(V)]) + "}{" + (LaTeX[x(A)^(2)]) + "}=\textit{a} ", " "}}, "l") → Conclusions2