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

配方法

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a=

b=

c=

$ |a|越小，開口越大 $

a = 4 (slider from -10 to 10, step 1)
b = 2 (slider from -10 to 10, step 0.1)
c = 1 (slider from -5 to 5, step 0.1)
f(x) = a * x^(2) + b * x + c
L: x = (-b) / (2 * a)
text5: "y=f(x)=" + a + "x²" + (If[b > 0, "+", "-"]) + (abs(b)) + "x" + (If[c > 0, "+", "-"]) + (abs(c))
V: ((-b) / (2 * a), (4 * a * c - b^(2)) / (4 * a))
text6: "f(x)=" + a + "x²" + (If[b < 0, "-", "+"]) + (abs(b)) + "x" + (If[c < 0, "-", "+"]) + (abs(c))
text9: "對稱軸x=" + ((-b) / (2 * a))
text10: "V(\frac{" + (-b) + "}{" + (2 * a) + "},\frac{4×(" + a + ")×(" + c + ")-" + (b^(2)) + "}{4*" + a + "})"
D: (0, c)
text11: "(0," + (LaTeX[c]) + ")"
text12: "$ V" + (LaTeX[V]) + " $"
k: (4 * a * c - b^(2)) / (4 * a)
text13: "=" + (LaTeX[a]) + "(x" + (LaTeX[If[a * b > 0, "+", "-"]]) + "" + (LaTeX[FractionText[abs(b / (2 * a))]]) + ")²" + (LaTeX[If[k < 0, "-", "+"]]) + "" + (LaTeX[FractionText[abs(k)]]) + ""
d = true
e = true
g = false
A, B = Root(f)
text16: "A" + (LaTeX[A]) + ""
text17: "B" + (LaTeX[B]) + ""
h = true
i = false
n = 0 (slider from 0 to 4, step 1)
inputBox1 = Textfield(a)
inputBox2 = Textfield(b)
inputBox3 = Textfield(c)
i_2 = false
Q_2: 0.4 * Corner[2] + 0.6 * 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])))
text7: "=" + (LaTeX[a]) + "(x²" + (LaTeX[If[b / a < 0, "-", "+"]]) + "" + (LaTeX[FractionText[abs(b / a)]]) + "x)" + (LaTeX[If[c > 0, "+", "-"]]) + "" + (LaTeX[c]) + ""
text8: "=" + (LaTeX[a]) + "［x²" + (LaTeX[If[b / a < 0, "-", "+"]]) + "" + (LaTeX[FractionText[abs(b / a)]]) + "x+\left(  \frac{" + (LaTeX[FractionText[b / a]]) + "}{" + (LaTeX[2]) + "} \right)² ］" + (LaTeX[If[c < 0, "-", "+"]]) + "" + (LaTeX[abs(c)]) + "" + (LaTeX[If[a > 0, "-", "+"]]) + "" + (LaTeX[FractionText[abs(b^(2) / (4 * a))]]) + ""
text14: "頂點V(" + (LaTeX[FractionText[(-b) / (2 * a)]]) + "," + (LaTeX[FractionText[k]]) + ")"