Kvadratické nerovnice

Príklad č.

Vrchol

Korene odpovedajúcej rovnice

Vrchol odpovedajúcej paraboly

Graf kvadratickej funkcie

Riešenie nerovnice

Riešte kvadratickú nerovnicu

C12: -8
B12: 6
A12: -1
C11: 5
B11: -4
A11: 1
C10: 3
B10: -5
A10: 1
C6: -3
B6: -2
A6: 2
C5: -3
B5: 3
A5: -1
C4: 6
B4: -7
A4: 1
K = 4 (slider from 1 to 12, step 1)
C3: 1
B3: -4
A3: 1
C2: -1
B2: 3
A2: -1
C1: 10
B1: -7
A1: 1
A7: 1
A8: 1
A9: -3
B7: -8
B9: 8
C7: 10
B8: -6
C8: 8
C9: -1
matica_3: {{A1, B1, C1}, {A2, B2, C2}, {A3, B3, C3}, {A4, B4, C4}, {A5, B5, C5}, {A6, B6, C6}, {A7, B7, C7}, {A8, B8, C8}, {A9, B9, C9}, {A10, B10, C10}, {A11, B11, C11}, {A12, B12, C12}}
matica_2: {{A1, B1, C1}, {A2, B2, C2}, {A3, B3, C3}, {A4, B4, C4}, {A5, B5, C5}, {A6, B6, C6}, {A7, B7, C7}, {A8, B8, C8}, {A9, B9, C9}}
matica_1: {{A1, B1, C1}, {A2, B2, C2}, {A3, B3, C3}, {A4, B4, C4}, {A5, B5, C5}, {A6, B6, C6}}
Zoznam_1 = Element(matica_3, K)
b = Element(Zoznam_1, 2)
c = Element(Zoznam_1, 3)
a = Element(Zoznam_1, 1)
f(x) = (a * x^(2)) + (b * x) + c
x_1, x_2 = Root(f)
text1 = SurdText(x(x_1))
text2 = SurdText(x(x_2))
text4: "x_1=" + (LaTeX[text1]) + ""
text5: "x_2=" + (LaTeX[text2]) + ""
g = IFactor(f)
k: x(x_1) - 3
l: x(x_2) + 3
text3: "" + (LaTeX[f]) + "≤0"
V = Extremum(f)
e = true
h = true
i = true
j = false
D: (b * b) - (4 * (a * c))
text6: "Diskriminant \; odpovedajúcej \;  kvadratickej \;  rovnice
 \\  D = " + (LaTeX[b]) + "^{2}-4×" + (LaTeX[a]) + "×" + (LaTeX[c]) + "=" + (LaTeX[D]) + ""
d: PolyLine[x_1, (-10 * x_1)] + PolyLine[x_2, (10 * x_2)]
o: PolyLine[x_1, (-10 * x_1)] + PolyLine[V, (10 * x_2)]
m = If(y(V) ≤ 0, PolyLine[x_1, x_2], PolyLine[x_1, (x(x_1) - 15, 0), (NaN, NaN), x_2, (x(x_2) + 15, 0)])
text9: "Príklad \; č. \; " + (LaTeX[K]) + ""
text8 = If(D < 0 ∧ c ≤ 0, "Riešením sú všetky reálne čísla", D < 0 ∧ c > 0, "Nerovnica nemá riešenie", D > 0 ∧ y(V) < 0, (((("Nerovnica má riešenie - uzavretý interval <" * x(x_1)) * " , ") * x(x_2)) * ">"), D > 0 ∧ y(V) ≥ 0, (((("Nerovnica má riešenie - zjednotenie intervalov (∞," * x(x_1)) * "> ,< ") * x(x_2)) * ", ∞)"))
n = If(y(V) ≤ 0, x > x(x_1) ∧ x < x(x_2), x < x(x_1) ∨ x > x(x_2))