二次不等式的圖形
Author: 藍邦偉  老師

二次不等式的圖形

≥0

≤0

x \in{  }R 

無解

c = 1 (slider from -5 to 5, step 0.1)
b = 2 (slider from -5 to 5, step 0.1)
a = 0.51 (slider from 0.01 to 5, step 0.1)
u = Vector((x(Corner[1.0]), 0.0), (x(Corner[3.0]), 0.0))
v = Vector((0.0, y(Corner[1.0])), (0.0, y(Corner[3.0])))
α = NaN (slider from -5 to 5, step 0.1)
β = NaN (slider from -5 to 5, step 0.1)
γ = NaN (slider from -5 to 5, step 0.1)
f(x) = a * x^(2.0) + b * x + c
A, B, C = Intersect(f, b_1)
A_1 = Corner(1.0)
A_2 = Corner(2.0)
A_3: Corner[1.0] + (0.0, 3.0)
A_4: Corner[2.0] + (0.0, 3.0)
A_0: (4.0 * Corner[1.0] + Corner[4.0]) / 5.0
w = Vector((x(Corner[1.0]), y(A_0)), (x(Corner[2.0]), y(A_0)))
P: (x(A), y(A_0))
Q: (x(B), y(A_0))
c_1 = Segment(A_3, A_4)
g = true
h = false
i = Segment(Q, P)
文字1: "f(x)=" + a + "x²" + (If[b < 0.0, "-", "+"]) + (abs(b)) + "x" + (If[c < 0.0, "-", "+"]) + (abs(c))
d: b^(2.0) - 4.0 * a * c
x_1: (-(b) - sqrt(d)) / 2.0 * a
x_2: (-(b) + sqrt(d)) / 2.0 * a
e = Vector(Q, (x(Corner[2.0]), y(A_0)))
文字2: "x≤" + x_1 + "∨x≥" + x_2
文字5: "x= \frac{" + (If[b < 0.0, " ", "-"]) + (abs(b)) + "  }{" + (2.0 * a) + " }=" + (-(b) / (2.0 * a))
文字3: x(P) + "≤x≤" + (x(Q))
多邊形1, a_1, a_2, a_4, a_3 = Polygon(A_1, A_2, A_4, A_3)
k = Vector(P, (x(Corner[1.0]), y(A_0)))