Nr. |
Polynomform |
Scheitelpunktform |
Linearfaktoren |
Schnittpunkte
|
Scheitelpunkt |
|
x-Achse |
y-Achse |
1.) |
f(x) = 0.5 x2 - 4 x + 7.5 |
f(x) = 0.5 (x - 4)2 - 0.5 |
f(x) = 0.5 (x - 5) (x - 3) |
x1 = 5 |
x2 = 3 |
y = 7.5 |
SP = (4 / -0.5 ) |
2.) |
f(x) = -0.5 x2 - 6.5 x - 21 |
f(x) = -0.5 (x + 6.5)2 + 0.125 |
f(x) = -0.5 (x + 7) (x + 6) |
x1 = -7 |
x2 = -6 |
y = -21 |
SP = (-6.5 / 0.125 ) |
3.) |
f(x) = -0.667 x2 - 6 x - 12 |
f(x) = -0.667 (x + 4.5)2 + 1.5 |
f(x) = -0.667 (x + 6) (x + 3) |
x1 = -6 |
x2 = -3 |
y = -12 |
SP = (-4.5 / 1.5 ) |
4.) |
f(x) = 0.5 x2 - 2 |
f(x) = 0.5 x2 - 2 |
f(x) = 0.5 (x + 2) (x - 2) |
x1 = -2 |
x2 = 2 |
y = -2 |
SP = (-0 / -2 ) |
5.) |
f(x) = 1 x2 + 2 x |
f(x) = 1 (x + 1)2 - 1 |
f(x) = 1 (x + 2) x |
x1 = -2 |
x2 = 0 |
y = -0 |
SP = (-1 / -1 ) |
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) = -0.333 x2 + 0.333 x + 10 |
f(x) = -0.333 (x - 0.5)2 + 10.083 |
f(x) = -0.333 (x - 6) (x + 5) |
x1 = 6 |
x2 = -5 |
y = 10 |
SP = (0.5 / 10.083 ) |
8.) |
f(x) = 0.5 x2 + 4.5 x + 7 |
f(x) = 0.5 (x + 4.5)2 - 3.125 |
f(x) = 0.5 (x + 2) (x + 7) |
x1 = -2 |
x2 = -7 |
y = 7 |
SP = (-4.5 / -3.125 ) |
9.) |
f(x) = 1 x2 - 6 x |
f(x) = 1 (x - 3)2 - 9 |
f(x) = 1 x (x - 6) |
x1 = 0 |
x2 = 6 |
y = 0 |
SP = (3 / -9 ) |
10.) |
f(x) = 2 x2 - 4 x |
f(x) = 2 (x - 1)2 - 2 |
f(x) = 2 x (x - 2) |
x1 = -0 |
x2 = 2 |
y = -0 |
SP = (1 / -2 ) |
11.) |
f(x) = 0.333 x2 + 2.667 x + 4 |
f(x) = 0.333 (x + 4)2 - 1.333 |
f(x) = 0.333 (x + 6) (x + 2) |
x1 = -6 |
x2 = -2 |
y = 4 |
SP = (-4 / -1.333 ) |
12.) |
f(x) = 1.5 x2 - 7.5 x + 9 |
f(x) = 1.5 (x - 2.5)2 - 0.375 |
f(x) = 1.5 (x - 3) (x - 2) |
x1 = 3 |
x2 = 2 |
y = 9 |
SP = (2.5 / -0.375 ) |
13.) |
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 ) |
14.) |
f(x) = -3 x2 + 12 x |
f(x) = -3 (x - 2)2 + 12 |
f(x) = -3 x (x - 4) |
x1 = -0 |
x2 = 4 |
y = 0 |
SP = (2 / 12 ) |
15.) |
f(x) = -1 x2 - 6 x + 7 |
f(x) = -1 (x + 3)2 + 16 |
f(x) = -1 (x - 1) (x + 7) |
x1 = 1 |
x2 = -7 |
y = 7 |
SP = (-3 / 16 ) |
16.) |
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 ) |
17.) |
f(x) = 1.5 x2 + 12 x + 10.5 |
f(x) = 1.5 (x + 4)2 - 13.5 |
f(x) = 1.5 (x + 1) (x + 7) |
x1 = -1 |
x2 = -7 |
y = 10.5 |
SP = (-4 / -13.5 ) |
18.) |
f(x) = 1.5 x2 + 1.5 x - 18 |
f(x) = 1.5 (x + 0.5)2 - 18.375 |
f(x) = 1.5 (x - 3) (x + 4) |
x1 = 3 |
x2 = -4 |
y = -18 |
SP = (-0.5 / -18.375 ) |
19.) |
f(x) = 1 x2 - 5 x + 4 |
f(x) = 1 (x - 2.5)2 - 2.25 |
f(x) = 1 (x - 4) (x - 1) |
x1 = 4 |
x2 = 1 |
y = 4 |
SP = (2.5 / -2.25 ) |
20.) |
f(x) = -0.75 x2 - 3.75 x - 4.5 |
f(x) = -0.75 (x + 2.5)2 + 0.188 |
f(x) = -0.75 (x + 3) (x + 2) |
x1 = -3 |
x2 = -2 |
y = -4.5 |
SP = (-2.5 / 0.188 ) |
21.) |
f(x) = -1 x2 - 10 x - 21 |
f(x) = -1 (x + 5)2 + 4 |
f(x) = -1 (x + 7) (x + 3) |
x1 = -7 |
x2 = -3 |
y = -21 |
SP = (-5 / 4 ) |
22.) |
f(x) = -1.5 x2 - 1.5 x + 9 |
f(x) = -1.5 (x + 0.5)2 + 9.375 |
f(x) = -1.5 (x - 2) (x + 3) |
x1 = 2 |
x2 = -3 |
y = 9 |
SP = (-0.5 / 9.375 ) |
23.) |
f(x) = -1 x2 + 4 x + 21 |
f(x) = -1 (x - 2)2 + 25 |
f(x) = -1 (x - 7) (x + 3) |
x1 = 7 |
x2 = -3 |
y = 21 |
SP = (2 / 25 ) |
24.) |
f(x) = -1 x2 - 2 x + 15 |
f(x) = -1 (x + 1)2 + 16 |
f(x) = -1 (x - 3) (x + 5) |
x1 = 3 |
x2 = -5 |
y = 15 |
SP = (-1 / 16 ) |
25.) |
f(x) = -0.75 x2 + 3.75 x |
f(x) = -0.75 (x - 2.5)2 + 4.688 |
f(x) = -0.75 (x - 5) x |
x1 = 5 |
x2 = 0 |
y = -0 |
SP = (2.5 / 4.688 ) |
26.) |
f(x) = 0.333 x2 - 1 x - 3.333 |
f(x) = 0.333 (x - 1.5)2 - 4.083 |
f(x) = 0.333 (x - 5) (x + 2) |
x1 = 5 |
x2 = -2 |
y = -3.333 |
SP = (1.5 / -4.083 ) |
27.) |
f(x) = 0.667 x2 - 6 x + 13.333 |
f(x) = 0.667 (x - 4.5)2 - 0.167 |
f(x) = 0.667 (x - 4) (x - 5) |
x1 = 4 |
x2 = 5 |
y = 13.333 |
SP = (4.5 / -0.167 ) |
28.) |
f(x) = 0.75 x2 - 7.5 x + 18 |
f(x) = 0.75 (x - 5)2 - 0.75 |
f(x) = 0.75 (x - 6) (x - 4) |
x1 = 6 |
x2 = 4 |
y = 18 |
SP = (5 / -0.75 ) |
29.) |
f(x) = 1 x2 + 8 x + 15 |
f(x) = 1 (x + 4)2 - 1 |
f(x) = 1 (x + 5) (x + 3) |
x1 = -5 |
x2 = -3 |
y = 15 |
SP = (-4 / -1 ) |
30.) |
f(x) = -1 x2 + 3 x + 10 |
f(x) = -1 (x - 1.5)2 + 12.25 |
f(x) = -1 (x + 2) (x - 5) |
x1 = -2 |
x2 = 5 |
y = 10 |
SP = (1.5 / 12.25 ) |