一元二次不等式的圖形
Author: 藍邦偉  老師

一元二次不等式的圖形

≥0

≤0

$ a= $

$ b= $

$ c= $

a

b

c

$ 無解 $

$ x∈\mathbb{R} $

k = 6 (slider from 1 to 30, step 1)
a = 2
c = 1 (slider from -5 to 5, step 0.1)
b = 5 (slider from -5 to 5, step 0.1)
u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
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) + b * x + c
A, B, C = Intersect(f, b_1)
A_1 = Corner(1)
A_2 = Corner(2)
A_3: Corner[1] + (0, 3)
A_4: Corner[2] + (0, 3)
A_0: (4 * Corner[1] + Corner[4]) / 5
w = Vector((x(Corner[1]), y(A_0)), (x(Corner[2]), y(A_0)))
P: (x(A), y(A_0))
Q: (x(B), y(A_0))
g = false
h = true
i = Segment(Q, P)
d: b^(2) - 4 * a * c
x_1: (-b - sqrt(d)) / 2 * a
x_2: (-b + sqrt(d)) / 2 * a
e = Vector(Q, (x(Corner[2]), y(A_0)))
多邊形1, a_1, a_2, a_4, a_3 = Polygon(A_1, A_2, A_4, A_3)
k_1 = Vector(P, (x(Corner[1]), y(A_0)))
t_f: "$ f(x)=" + (LaTeX[If[abs(a) ≠ 1, FractionText[a], If[a ≟ -1, "-", ""]]]) + " x^2" + (LaTeX[If[b ≟ 0, "", If[b ≟ 1, "+x", If[b ≟ -1, "-x", If[b > 0, "+" * abs(b) * "x", -abs(b) * "x"]]]]]) + "" + (LaTeX[If[c > 0, "+" * c, If[c < 0, "-" * abs(c), ""]]]) + "$"
inputBox1 = Textfield(a)
inputBox2 = Textfield(b)
inputBox3 = Textfield(c)
text1: "$⇒ " + (LaTeX[x(P)]) + "≤x≤" + (LaTeX[x(Q)]) + " $"
text2: "$ x≤" + (LaTeX[x_1]) + " \;或\;x≥" + (LaTeX[x_2]) + "$"
text3: "$ x=\frac{-" + (LaTeX[b]) + "}{" + (LaTeX[2 * a]) + "} =" + (LaTeX[FractionText[(-b) / (2 * a)]]) + "$"
gcd = GCD(2 * a, b)
D = (3.4185323898757325, -4.2331649105272575)