切线与法线作图练习：随机二次函数点的几何辨析

GeoGebra 命令及参数

1. Random(1, 10) → whatweget
2. Random(-5, 5) → a_{1}
3. If(a_{1} ≠ 0, a_{1}, 1) → a
4. Random(-10, 10) → b
5. Random(-20, 20) → c
6. Random(-7, 7) → xap_{1}
7. If(whatweget ≟ 1, 1 / sqrt(Simplify[(abs(a) * x) + abs(c)]), whatweget ≟ 6, 1 / Simplify[(a * x) + c], whatweget ≟ 7, 1 / Simplify[(a * x^(2)) + c], whatweget ≟ 8, sqrt(Simplify[(a * x) + abs(c)]), whatweget ≟ 9, sqrt(Simplify[(a * x^(2)) + abs(c)]), whatweget ≟ 10, Factor[((a * x) + b)^(2)], whatweget ≟ 2, Simplify[(a * x^(2)) + c], whatweget ≟ 3, Simplify[(a * x^(3)) + c], whatweget ≟ 4, Simplify[(a * x^(2)) + (b * x) + c], whatweget ≟ 5, Simplify[(a * x^(3)) + (b * x) + c]) → f
8. If(whatweget ≟ 1, Random[1, 7], whatweget ≟ 8 ∧ a ≥ 0, Random[1, 7], whatweget ≟ 8 ∧ a < 0, Random[-7, -1], whatweget ≟ 9 ∧ a < 0, Random[0, floor(sqrt(abs(c) / abs(a)))], xap_{1}) → xap
9. SurdText(tangslpe) → tangslpetxt
10. Textfield(yourtangentslope) → InputBox1
11. Textfield(yournormalslope) → InputBox2
12. Textfield(yourtangentline) → InputBox3
13. Textfield(yournormalline) → InputBox4