Nr. |
Polynomform |
Scheitelpunktform |
Linearfaktoren |
Schnittpunkte
|
Scheitelpunkt |
|
x-Achse |
y-Achse |
1.) |
f(x) = 3 x2 + 9 x + 6 |
f(x) = 3 (x + 1.5)2 - 0.75 |
f(x) = 3 (x + 2) (x + 1) |
x1 = -2 |
x2 = -1 |
y = 6 |
SP = (-1.5 / -0.75 ) |
2.) |
f(x) = 2 x2 - 26 x + 84 |
f(x) = 2 (x - 6.5)2 - 0.5 |
f(x) = 2 (x - 6) (x - 7) |
x1 = 6 |
x2 = 7 |
y = 84 |
SP = (6.5 / -0.5 ) |
3.) |
f(x) = -1 x2 + 5 x + 6 |
f(x) = -1 (x - 2.5)2 + 12.25 |
f(x) = -1 (x + 1) (x - 6) |
x1 = -1 |
x2 = 6 |
y = 6 |
SP = (2.5 / 12.25 ) |
4.) |
f(x) = -0.25 x2 + 3 x - 8.75 |
f(x) = -0.25 (x - 6)2 + 0.25 |
f(x) = -0.25 (x - 5) (x - 7) |
x1 = 5 |
x2 = 7 |
y = -8.75 |
SP = (6 / 0.25 ) |
5.) |
f(x) = -0.5 x2 - 0.5 x |
f(x) = -0.5 (x + 0.5)2 + 0.125 |
f(x) = -0.5 x (x + 1) |
x1 = 0 |
x2 = -1 |
y = 0 |
SP = (-0.5 / 0.125 ) |
6.) |
f(x) = 1 x2 - 6 x + 5 |
f(x) = 1 (x - 3)2 - 4 |
f(x) = 1 (x - 5) (x - 1) |
x1 = 5 |
x2 = 1 |
y = 5 |
SP = (3 / -4 ) |
7.) |
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 ) |
8.) |
f(x) = 0.75 x2 - 9 x + 26.25 |
f(x) = 0.75 (x - 6)2 - 0.75 |
f(x) = 0.75 (x - 7) (x - 5) |
x1 = 7 |
x2 = 5 |
y = 26.25 |
SP = (6 / -0.75 ) |
9.) |
f(x) = -0.667 x2 - 7.333 x - 18.667 |
f(x) = -0.667 (x + 5.5)2 + 1.5 |
f(x) = -0.667 (x + 4) (x + 7) |
x1 = -4 |
x2 = -7 |
y = -18.667 |
SP = (-5.5 / 1.5 ) |
10.) |
f(x) = 1 x2 + 3 x - 18 |
f(x) = 1 (x + 1.5)2 - 20.25 |
f(x) = 1 (x - 3) (x + 6) |
x1 = 3 |
x2 = -6 |
y = -18 |
SP = (-1.5 / -20.25 ) |
11.) |
f(x) = 0.25 x2 - 2.25 x + 5 |
f(x) = 0.25 (x - 4.5)2 - 0.063 |
f(x) = 0.25 (x - 4) (x - 5) |
x1 = 4 |
x2 = 5 |
y = 5 |
SP = (4.5 / -0.063 ) |
12.) |
f(x) = -2 x2 + 98 |
f(x) = -2 x2 + 98 |
f(x) = -2 (x + 7) (x - 7) |
x1 = -7 |
x2 = 7 |
y = 98 |
SP = (-0 / 98 ) |
13.) |
f(x) = 0.667 x2 + 2 x - 2.667 |
f(x) = 0.667 (x + 1.5)2 - 4.167 |
f(x) = 0.667 (x - 1) (x + 4) |
x1 = 1 |
x2 = -4 |
y = -2.667 |
SP = (-1.5 / -4.167 ) |
14.) |
f(x) = 0.333 x2 + 2.333 x |
f(x) = 0.333 (x + 3.5)2 - 4.083 |
f(x) = 0.333 (x + 7) x |
x1 = -7 |
x2 = -0 |
y = 0 |
SP = (-3.5 / -4.083 ) |
15.) |
f(x) = -0.25 x2 - 1.25 x - 1 |
f(x) = -0.25 (x + 2.5)2 + 0.563 |
f(x) = -0.25 (x + 4) (x + 1) |
x1 = -4 |
x2 = -1 |
y = -1 |
SP = (-2.5 / 0.563 ) |
16.) |
f(x) = -2 x2 - 6 x - 4 |
f(x) = -2 (x + 1.5)2 + 0.5 |
f(x) = -2 (x + 2) (x + 1) |
x1 = -2 |
x2 = -1 |
y = -4 |
SP = (-1.5 / 0.5 ) |
17.) |
f(x) = -2 x2 + 8 x + 42 |
f(x) = -2 (x - 2)2 + 50 |
f(x) = -2 (x + 3) (x - 7) |
x1 = -3 |
x2 = 7 |
y = 42 |
SP = (2 / 50 ) |
18.) |
f(x) = 0.5 x2 + 2 x - 10.5 |
f(x) = 0.5 (x + 2)2 - 12.5 |
f(x) = 0.5 (x - 3) (x + 7) |
x1 = 3 |
x2 = -7 |
y = -10.5 |
SP = (-2 / -12.5 ) |
19.) |
f(x) = -0.5 x2 - 0.5 x + 21 |
f(x) = -0.5 (x + 0.5)2 + 21.125 |
f(x) = -0.5 (x + 7) (x - 6) |
x1 = -7 |
x2 = 6 |
y = 21 |
SP = (-0.5 / 21.125 ) |
20.) |
f(x) = -2 x2 + 26 x - 84 |
f(x) = -2 (x - 6.5)2 + 0.5 |
f(x) = -2 (x - 6) (x - 7) |
x1 = 6 |
x2 = 7 |
y = -84 |
SP = (6.5 / 0.5 ) |
21.) |
f(x) = -0.25 x2 + 3.25 x - 10.5 |
f(x) = -0.25 (x - 6.5)2 + 0.063 |
f(x) = -0.25 (x - 6) (x - 7) |
x1 = 6 |
x2 = 7 |
y = -10.5 |
SP = (6.5 / 0.063 ) |
22.) |
f(x) = -0.333 x2 - 1.667 x + 4.667 |
f(x) = -0.333 (x + 2.5)2 + 6.75 |
f(x) = -0.333 (x + 7) (x - 2) |
x1 = -7 |
x2 = 2 |
y = 4.667 |
SP = (-2.5 / 6.75 ) |
23.) |
f(x) = 3 x2 + 15 x - 18 |
f(x) = 3 (x + 2.5)2 - 36.75 |
f(x) = 3 (x - 1) (x + 6) |
x1 = 1 |
x2 = -6 |
y = -18 |
SP = (-2.5 / -36.75 ) |
24.) |
f(x) = -2 x2 - 12 x |
f(x) = -2 (x + 3)2 + 18 |
f(x) = -2 x (x + 6) |
x1 = -0 |
x2 = -6 |
y = -0 |
SP = (-3 / 18 ) |
25.) |
f(x) = 0.25 x2 + 0.25 x - 7.5 |
f(x) = 0.25 (x + 0.5)2 - 7.563 |
f(x) = 0.25 (x + 6) (x - 5) |
x1 = -6 |
x2 = 5 |
y = -7.5 |
SP = (-0.5 / -7.563 ) |
26.) |
f(x) = 0.5 x2 + 4 x + 3.5 |
f(x) = 0.5 (x + 4)2 - 4.5 |
f(x) = 0.5 (x + 1) (x + 7) |
x1 = -1 |
x2 = -7 |
y = 3.5 |
SP = (-4 / -4.5 ) |
27.) |
f(x) = 0.5 x2 - 0.5 x - 1 |
f(x) = 0.5 (x - 0.5)2 - 1.125 |
f(x) = 0.5 (x - 2) (x + 1) |
x1 = 2 |
x2 = -1 |
y = -1 |
SP = (0.5 / -1.125 ) |
28.) |
f(x) = -0.333 x2 + 0.333 |
f(x) = -0.333 x2 + 0.333 |
f(x) = -0.333 (x + 1) (x - 1) |
x1 = -1 |
x2 = 1 |
y = 0.333 |
SP = (-0 / 0.333 ) |
29.) |
f(x) = 1 x2 + 8 x + 12 |
f(x) = 1 (x + 4)2 - 4 |
f(x) = 1 (x + 2) (x + 6) |
x1 = -2 |
x2 = -6 |
y = 12 |
SP = (-4 / -4 ) |
30.) |
f(x) = -0.667 x2 - 2.667 x |
f(x) = -0.667 (x + 2)2 + 2.667 |
f(x) = -0.667 x (x + 4) |
x1 = -0 |
x2 = -4 |
y = -0 |
SP = (-2 / 2.667 ) |