拋物線的性質
Author: 藍邦偉  老師

拋物線的性質：

$F$

開口左右的拋物線

$F$

開口上下的拋物線

V(

h

,

k

)

c=

c

h = 1 (slider from -5 to 5, step 1)
c = 1 (slider from -5 to 5, step 0.2)
k = 1 (slider from -5 to 5, step 1)
a: x = h - c
P_1: (x(Corner[1]), 0)
P_2: (x(Corner[2]), 0)
u = Vector(P_1, P_2)
P_3: (0, y(Corner[1]))
P_4: (0, y(Corner[3]))
v = Vector(P_3, P_4)
Γ: (y - k)^(2) = 4 * c * (x - h)
F: (h + c, k)
b: x = k + c
A: (h + c, k + 2 * c)
B: (h + c, k - 2 * c)
d = Segment(A, B)
C = Midpoint(A, F)
D = Midpoint(F, B)
V: (h, k)
A_1: (h - c, k)
e: y = k
f = LineBisector(A, C)
g = LineBisector(C, F)
i = LineBisector(F, D)
j = LineBisector(D, B)
l = LineBisector(V, F)
E = Intersect(f, l)
p = CircleArc(E, C, A)
G = Intersect(g, l)
H = Intersect(i, l)
I = Intersect(j, l)
q = CircleArc(G, F, C)
r = CircleArc(H, D, F)
s = CircleArc(I, B, D)
t = CircleArc(H, F, V)
m = LineBisector(A_1, V)
J = Intersect(i, m)
c_1 = CircleArc(J, V, A_1)
o = false
Γ_2: (x - h)^(2) = 4 * c * (y - k)
F_2: (h, k + c)
L_2: y = k - c
l_2: x = h
V_2: (h, k)
A_2: (h, k - c)
U_1: (h - 2 * c, k + c)
K = Mirror(U_1, l_2)
L = Midpoint(U_1, F_2)
M = Midpoint(F_2, K)
n = Segment(U_1, K)
a_1 = LineBisector(U_1, L)
b_1 = LineBisector(L, F_2)
d_1 = LineBisector(F_2, M)
e_1 = LineBisector(M, K)
f_1 = LineBisector(F_2, V_2)
N = Intersect(a_1, f_1)
O = Intersect(b_1, f_1)
P = Intersect(d_1, f_1)
Q = Intersect(e_1, f_1)
g_1 = CircleArc(N, L, U_1)
h_1 = CircleArc(O, F_2, L)
k_1 = CircleArc(P, M, F_2)
p_1 = CircleArc(Q, K, M)
q_1 = CircleArc(P, F_2, V_2)
i_1 = LineBisector(V_2, A_2)
R = Intersect(d_1, i_1)
r_1 = CircleArc(R, V_2, A_2)
w = true
T_1 = Corner(1)
T_4 = Corner(4)
T_2: (3 * Corner[1] + Corner[2]) / 4
T_3: (3 * Corner[4] + Corner[3]) / 4
多邊形1, t_1, t_2, t_3, t_4 = Polygon(T_1, T_2, T_3, T_4)
j_1 = Segment(T_2, T_3)
inputBox1 = Textfield(h)
inputBox2 = Textfield(k)
inputBox3 = Textfield(c)
S = (-3.8110214691658824, 2.6381709814673733)
text6: "$" + (LaTeX[If[h ≟ 0, "", "("]]) + "x" + (LaTeX[If[h > 0, "-" * abs(h), If[h ≟ 0, "", "+" * abs(h)]]]) + "" + (LaTeX[If[h ≟ 0, "^2", ")^2"]]) + "=" + (LaTeX[4 * c]) + "" + (LaTeX[If[k ≟ 0, "", "("]]) + "y" + (LaTeX[If[k > 0, "-" * abs(k), If[k < 0, "+" * abs(k), ""]]]) + "" + (LaTeX[If[k ≟ 0, "", ")"]]) + "$"
text5: "" + (LaTeX[If[k ≟ 0, "", "("]]) + "y" + (LaTeX[If[k > 0, "-" * abs(k), If[k ≟ 0, "", "+" * abs(k)]]]) + "" + (LaTeX[If[k ≟ 0, "^2", ")^2"]]) + "=" + (LaTeX[4 * c]) + "" + (LaTeX[If[h ≟ 0, "", "("]]) + "x" + (LaTeX[If[h > 0, "-" * abs(h), If[h < 0, "+" * abs(h), ""]]]) + "" + (LaTeX[If[h ≟ 0, "", ")"]]) + ""