二次函数增减性的图形探究：开口方向与单调区间

GeoGebra 命令及参数

1. Corner(5) → AppSize
2. Polygon({ViewCorner1_{1}, (x(ViewCorner3_{1}), y(ViewCorner1_{1})), ViewCorner3_{1}, (x(ViewCorner1_{1}), y(ViewCorner3_{1}))}) → q1_{1}
3. Text("x", (12, 0.1), true, true, 0, 0) → text1_{1}
4. Flatten(Sequence[Sequence[(ii, jj), ii, -11, 11], jj, -5, 5]) → gridPoints
5. Point(gridPoints) → P2
6. Text("y", (yax, 6), true, true, 0, 0) → text2_{1}
7. Sequence((-yax) + ii - 10, ii, 0, 20) → xNums, {-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
8. Sequence(Text[(-yax) + ii - 10, (-10 + ii, 0), true, true, 0, -1], ii, If[Mod[yax, 2] ≟ 0, 1, 0], 20, 2) → xAxisNumbers
9. Sequence(Segment[(ii, -0.1), (ii, 0.1)], ii, If[Mod[yax, 2] ≟ 1, -10, -9], 10, 2) → ticks
10. Point(gridPoints) → P1
11. If(y(P1) ≠ y(P2), (("(-\infty," * x(P1)) * ")")) → Text1'
12. If(y(P1) ≠ y(P2), (("(" * x(P1)) * ",\infty)")) → Text2'
13. Text(Text1, Pos1, true, true, 0, 0) → text1
14. Text(Text2, Pos2, true, true, 0, 0) → text2
15. Text(Text2', Pos4, true, true, 0, 0) → text3
16. Text(Text1', Pos3, true, true, 0, 0) → text4
17. If(f(x(P1) - 1) ≟ f(x(P1)), 2, If[f(x(P1) - 1) ≤ f(x(P1)), 3, 1]) → colorLeft
18. If(f(x(P1) + 1) ≟ f(x(P1)), 2, If[f(x(P1) + 1) ≤ f(x(P1)), 1, 3]) → colorRight
19. Translate(hGuideline, Vector[(Vector[Corner[1], Corner[3]] / 500 * 16)]) → hGuideline'
20. Segment((yax, y(ViewCorner1_{1}) + 0.05), (yax, y(ViewCorner3_{1}) - 0.05)) → yAxisFake_{1}
21. Segment((x(ViewCorner1_{1}) + 0.05, 0), (x(ViewCorner3_{1}) - 0.05, 0)) → xAxisFake_{1}
22. circlePixels(P2, 9 + (7 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingObject