多項式(18)
Author: 藍邦偉　老師

x

y

$ f(x)=ax+b $

g(x)=c(x-c)³

h(x)=dx⁴+e

(A) a>0

(B)b>0

$ (C)c>0 $

$ (D)e=-c⁴ $

(E)d>1

$ (A)直線斜率為負⇒a<0 $

$ (B)直線的y截距為正⇒b>0 $

$ (C) 三次函數的x越大y越小⇒c<0$

$ (D)h(0)=g(0) ⇒e=-c⁴$

$ h(x)=dx⁴-c⁴ =(x+c)(x-c)(dx²+c²)$

$ (E)如圖，又B,C兩點的座標分別為(c,0)與(-c,0) $

$ =dx⁴+c²(1-d²)x-c⁴,比較係數得 1-d²=0$

$ d=±1 $

f(x) = -x + 1
A = Point(yAxis)
B = (-1, 0)
B' = Mirror(B, A)
E = (1.390678489295942, 0.4719501464139429)
D = (1, 0)
E' = Mirror(E, yAxis)
h = Polynomial({E, E', B, A, D})
n = 4 (slider from 0 to 9, step 1)
C_4 = (-9.94065700636129, 1.6980750663955788)
C_1: C_4 + (1.8, 0)
C_3: C_4 + (0, 0.8)
C_2: C_1 + C_3 - C_4
poly1, c, c_1, c_2, c_3 = Polygon(C_4, C_1, C_2, C_3)
v = Vector((0, -5), (0, y(Corner[3])))
F = Mirror(Mirror[B, A], A)
A' = Mirror(A, B)
G = (0.7963353224754431, -1.7903883595479488)
g = Polynomial({A, A', B, G})
u = Vector((-2, 0), (x(Corner[2]), 0))
H, C = Intersect(f, h)