Nr. |
Polynomform |
Scheitelpunktform |
Linearfaktoren |
Schnittpunkte
|
Scheitelpunkt |
|
x-Achse |
y-Achse |
1.) |
f(x) = -3 x2 + 3 x + 36 |
f(x) = -3 (x - 0.5)2 + 36.75 |
f(x) = -3 (x - 4) (x + 3) |
x1 = 4 |
x2 = -3 |
y = 36 |
SP = (0.5 / 36.75 ) |
2.) |
f(x) = -2 x2 - 14 x - 20 |
f(x) = -2 (x + 3.5)2 + 4.5 |
f(x) = -2 (x + 2) (x + 5) |
x1 = -2 |
x2 = -5 |
y = -20 |
SP = (-3.5 / 4.5 ) |
3.) |
f(x) = 0.333 x2 - 2.667 x + 2.333 |
f(x) = 0.333 (x - 4)2 - 3 |
f(x) = 0.333 (x - 1) (x - 7) |
x1 = 1 |
x2 = 7 |
y = 2.333 |
SP = (4 / -3 ) |
4.) |
f(x) = -1 x2 + 1 x + 12 |
f(x) = -1 (x - 0.5)2 + 12.25 |
f(x) = -1 (x + 3) (x - 4) |
x1 = -3 |
x2 = 4 |
y = 12 |
SP = (0.5 / 12.25 ) |
5.) |
f(x) = -2 x2 - 2 x + 12 |
f(x) = -2 (x + 0.5)2 + 12.5 |
f(x) = -2 (x - 2) (x + 3) |
x1 = 2 |
x2 = -3 |
y = 12 |
SP = (-0.5 / 12.5 ) |
6.) |
f(x) = 0.5 x2 - 3.5 x |
f(x) = 0.5 (x - 3.5)2 - 6.125 |
f(x) = 0.5 x (x - 7) |
x1 = 0 |
x2 = 7 |
y = 0 |
SP = (3.5 / -6.125 ) |
7.) |
f(x) = -0.25 x2 + 0.25 x + 1.5 |
f(x) = -0.25 (x - 0.5)2 + 1.563 |
f(x) = -0.25 (x - 3) (x + 2) |
x1 = 3 |
x2 = -2 |
y = 1.5 |
SP = (0.5 / 1.563 ) |
8.) |
f(x) = -0.25 x2 + 2 x - 3 |
f(x) = -0.25 (x - 4)2 + 1 |
f(x) = -0.25 (x - 6) (x - 2) |
x1 = 6 |
x2 = 2 |
y = -3 |
SP = (4 / 1 ) |
9.) |
f(x) = -1 x2 - 1 x + 2 |
f(x) = -1 (x + 0.5)2 + 2.25 |
f(x) = -1 (x + 2) (x - 1) |
x1 = -2 |
x2 = 1 |
y = 2 |
SP = (-0.5 / 2.25 ) |
10.) |
f(x) = 0.5 x2 + 1.5 x |
f(x) = 0.5 (x + 1.5)2 - 1.125 |
f(x) = 0.5 (x + 3) x |
x1 = -3 |
x2 = -0 |
y = 0 |
SP = (-1.5 / -1.125 ) |
11.) |
f(x) = 1 x2 - 25 |
f(x) = 1 x2 - 25 |
f(x) = 1 (x - 5) (x + 5) |
x1 = 5 |
x2 = -5 |
y = -25 |
SP = (-0 / -25 ) |
12.) |
f(x) = -0.25 x2 - 1.75 x |
f(x) = -0.25 (x + 3.5)2 + 3.063 |
f(x) = -0.25 (x + 7) x |
x1 = -7 |
x2 = -0 |
y = -0 |
SP = (-3.5 / 3.063 ) |
13.) |
f(x) = 1.5 x2 + 9 x + 7.5 |
f(x) = 1.5 (x + 3)2 - 6 |
f(x) = 1.5 (x + 5) (x + 1) |
x1 = -5 |
x2 = -1 |
y = 7.5 |
SP = (-3 / -6 ) |
14.) |
f(x) = -1 x2 + 9 x - 20 |
f(x) = -1 (x - 4.5)2 + 0.25 |
f(x) = -1 (x - 5) (x - 4) |
x1 = 5 |
x2 = 4 |
y = -20 |
SP = (4.5 / 0.25 ) |
15.) |
f(x) = -0.333 x2 + 3.667 x - 10 |
f(x) = -0.333 (x - 5.5)2 + 0.083 |
f(x) = -0.333 (x - 5) (x - 6) |
x1 = 5 |
x2 = 6 |
y = -10 |
SP = (5.5 / 0.083 ) |
16.) |
f(x) = 0.25 x2 - 2 x + 3 |
f(x) = 0.25 (x - 4)2 - 1 |
f(x) = 0.25 (x - 2) (x - 6) |
x1 = 2 |
x2 = 6 |
y = 3 |
SP = (4 / -1 ) |
17.) |
f(x) = -2 x2 - 16 x - 30 |
f(x) = -2 (x + 4)2 + 2 |
f(x) = -2 (x + 3) (x + 5) |
x1 = -3 |
x2 = -5 |
y = -30 |
SP = (-4 / 2 ) |
18.) |
f(x) = 0.5 x2 - 0.5 x - 3 |
f(x) = 0.5 (x - 0.5)2 - 3.125 |
f(x) = 0.5 (x - 3) (x + 2) |
x1 = 3 |
x2 = -2 |
y = -3 |
SP = (0.5 / -3.125 ) |
19.) |
f(x) = 1.5 x2 - 15 x + 31.5 |
f(x) = 1.5 (x - 5)2 - 6 |
f(x) = 1.5 (x - 3) (x - 7) |
x1 = 3 |
x2 = 7 |
y = 31.5 |
SP = (5 / -6 ) |
20.) |
f(x) = -0.5 x2 + 5 x - 12 |
f(x) = -0.5 (x - 5)2 + 0.5 |
f(x) = -0.5 (x - 6) (x - 4) |
x1 = 6 |
x2 = 4 |
y = -12 |
SP = (5 / 0.5 ) |
21.) |
f(x) = -3 x2 + 18 x |
f(x) = -3 (x - 3)2 + 27 |
f(x) = -3 x (x - 6) |
x1 = -0 |
x2 = 6 |
y = 0 |
SP = (3 / 27 ) |
22.) |
f(x) = -1 x2 + 7 x - 10 |
f(x) = -1 (x - 3.5)2 + 2.25 |
f(x) = -1 (x - 2) (x - 5) |
x1 = 2 |
x2 = 5 |
y = -10 |
SP = (3.5 / 2.25 ) |
23.) |
f(x) = 0.667 x2 + 2.667 x |
f(x) = 0.667 (x + 2)2 - 2.667 |
f(x) = 0.667 (x + 4) x |
x1 = -4 |
x2 = 0 |
y = -0 |
SP = (-2 / -2.667 ) |
24.) |
f(x) = -1 x2 - 1 x + 42 |
f(x) = -1 (x + 0.5)2 + 42.25 |
f(x) = -1 (x - 6) (x + 7) |
x1 = 6 |
x2 = -7 |
y = 42 |
SP = (-0.5 / 42.25 ) |
25.) |
f(x) = -1.5 x2 + 3 x + 12 |
f(x) = -1.5 (x - 1)2 + 13.5 |
f(x) = -1.5 (x + 2) (x - 4) |
x1 = -2 |
x2 = 4 |
y = 12 |
SP = (1 / 13.5 ) |
26.) |
f(x) = 0.333 x2 + 1.333 x - 1.667 |
f(x) = 0.333 (x + 2)2 - 3 |
f(x) = 0.333 (x - 1) (x + 5) |
x1 = 1 |
x2 = -5 |
y = -1.667 |
SP = (-2 / -3 ) |
27.) |
f(x) = 0.333 x2 + 3 x + 4.667 |
f(x) = 0.333 (x + 4.5)2 - 2.083 |
f(x) = 0.333 (x + 7) (x + 2) |
x1 = -7 |
x2 = -2 |
y = 4.667 |
SP = (-4.5 / -2.083 ) |
28.) |
f(x) = -0.667 x2 - 5.333 x - 4.667 |
f(x) = -0.667 (x + 4)2 + 6 |
f(x) = -0.667 (x + 7) (x + 1) |
x1 = -7 |
x2 = -1 |
y = -4.667 |
SP = (-4 / 6 ) |
29.) |
f(x) = 1 x2 - 16 |
f(x) = 1 x2 - 16 |
f(x) = 1 (x + 4) (x - 4) |
x1 = -4 |
x2 = 4 |
y = -16 |
SP = (-0 / -16 ) |
30.) |
f(x) = 1 x2 - 12 x + 35 |
f(x) = 1 (x - 6)2 - 1 |
f(x) = 1 (x - 7) (x - 5) |
x1 = 7 |
x2 = 5 |
y = 35 |
SP = (6 / -1 ) |