二次函數的圖形與配方法
Author: 藍邦偉　老師

y=f(x)=ax²+bx+c,a≠0

a>0:開口向上

a<0:開口向下

|a|越大，\;開口越小

二次函數的性質

圖形

性質

滑竿輸入

自行輸入

a=

b=

c=

$ |a|越小，\;開口越大 $

配方法

$ a= $

$ b= $

$ c= $

a = 1 (slider from -5 to 5, step 1)
b = 2 (slider from -10 to 10, step 1)
c = -3 (slider from -5 to 5, step 1)
f(x) = a * x^(2) + b * x + c
L: x = (-b) / (2 * a)
V: ((-b) / (2 * a), (4 * a * c - b^(2)) / (4 * a))
text16: "對稱軸x=" + ((-b) / (2 * a))
D: (0, c)
text11_1: "(0," + (LaTeX[c]) + ")"
k: (4 * a * c - b^(2)) / (4 * a)
d = true
e = false
A, B = Root(f)
h = true
i = false
n = 0 (slider from 0 to If[e ≟ true, 7, 5], step 1)
inputBox1 = Textfield(a)
inputBox2 = Textfield(b)
inputBox3 = Textfield(c)
i_2 = false
Q_2: 0.35 * Corner[2] + 0.65 * Corner[1]
Q_3: (x(Q_2), y(Corner[3]))
poly1, j, q_2, q_3, l = Polygon(Corner[1], Q_2, Q_3, Corner[4])
m = Segment(Q_2, Q_3)
u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
text25: "頂點V(" + (LaTeX[FractionText[(-b) / (2 * a)]]) + "," + (LaTeX[FractionText[k]]) + ")"
t_v: "$ V(" + (LaTeX[FractionText[x(V)]]) + " ," + (LaTeX[FractionText[y(V)]]) + ")$"
t_A: "A(" + (LaTeX[FractionText[x(A)]]) + "," + (LaTeX[FractionText[y(A)]]) + ")"
t_B: "B(" + (LaTeX[FractionText[x(B)]]) + "," + (LaTeX[FractionText[y(B)]]) + ")"
g = false
text17: "$V(\;\frac{" + (LaTeX[-b]) + "}{2×" + (LaTeX[If[a < 0, "(-"]]) + "" + (LaTeX[abs(a)]) + "" + (LaTeX[If[a < 0, ")"]]) + "}\;,\;\frac{4×" + (LaTeX[If[a < 0, "(-", ""]]) + "" + (LaTeX[abs(a)]) + "" + (LaTeX[If[a < 0, ")", ""]]) + "×" + (LaTeX[If[c < 0, "(", ""]]) + "" + (LaTeX[abs(c)]) + "" + (LaTeX[If[c < 0, ")", ""]]) + "-" + (LaTeX[If[b < 0, "(-"]]) + "" + (LaTeX[abs(b)]) + "" + (LaTeX[If[b < 0, ")"]]) + "^2}{4×" + (LaTeX[If[a < 0, "(-"]]) + "" + (LaTeX[abs(a)]) + "" + (LaTeX[If[a < 0, ")"]]) + "})$
$⇒V(" + (LaTeX[FractionText[x(V)]]) + "," + (LaTeX[FractionText[y(V)]]) + ")$"
text21: "f(x)=" + (LaTeX[If[abs(a) ≠ 1, FractionText[a], If[a ≟ 1, "", "-"]]]) + "x²" + (LaTeX[If[b < 0, "-", "+"]]) + "" + (LaTeX[FractionText[abs(b)]]) + "x" + (LaTeX[If[c < 0, "-", If[c > 0, "+", ""]]]) + "" + (LaTeX[If[c ≠ 0, abs(c), ""]]) + ""
text22: "\;\;\;=" + (LaTeX[If[abs(a) ≠ 1, FractionText[a], If[a ≟ 1, "", "-"]]]) + "(x²" + (LaTeX[If[b / a < 0, "-", "+"]]) + "" + (LaTeX[If[b / a ≠ 1, FractionText[abs(b / a)], ""]]) + "x)" + (LaTeX[If[c > 0, "+", If[c ≠ 0, "-", ""]]]) + "" + (LaTeX[If[c ≠ 0, abs(c), ""]]) + ""
text23: "\;\;=" + (LaTeX[If[abs(a) ≠ 1, FractionText[a], If[a ≟ 1, "", "-"]]]) + "［x²" + (LaTeX[If[b / a < 0, "-", "+"]]) + "" + (LaTeX[FractionText[abs(b / a)]]) + "x+\left(  \frac{" + (LaTeX[FractionText[abs(b / a)]]) + "}{" + (LaTeX[2]) + "} \right)² ］" + (LaTeX[If[c < 0, "-", "+"]]) + "" + (LaTeX[abs(c)]) + "" + (LaTeX[If[a > 0, "-", "+"]]) + "" + (LaTeX[FractionText[abs(b^(2) / (4 * a))]]) + ""
text24: "=" + (LaTeX[If[abs(a) ≠ 1, FractionText[a], If[a ≟ 1, "", "-"]]]) + "(x" + (LaTeX[If[a * b > 0, "+", "-"]]) + "" + (LaTeX[FractionText[abs(b / (2 * a))]]) + ")²" + (LaTeX[If[k < 0, "-", "+"]]) + "" + (LaTeX[FractionText[abs(k)]]) + ""