Einsen­de­auf­gabe ILS Mats 11a/0414 K05 Quadra­ti­sche Glei­chungen und Quadra­ti­sche Funk­tionen

Mats 11a / 0414 K05

1

a) y = 8x²

» nach oben geöffnet

» gestreckt

» S (0│0)

b) y = 0,5x² + 1

» nach oben geöffnet

» gestaucht

» S (0│1)

c) y = 6x² – 3

» nach oben geöffnet

» gestreckt

» S (0│-3)

y = 1,5 (x2 - 4x) +2

y = 1,5 (x2 - 4x + 0) +2

y = 1,5 (x2 - 4x + 22 - 22) + 2

y = 1,5 (x2 - 4x + 22) - 6 + 2

y = 1,5 (x - 2)2- 4

Nr.3

a) 12x + 2x2 = 54 │- 54

2x2 + 12x – 54 = 0 │: 2

x2 + 6x – 27 = 0

QE: (6/2)2 = 32

x2 + 6x + 0 - 27 =

x2 + 6x + 32 - 32 - 27 = 0

x2 + 6x + 32 - 32 - 27 =

(x + 3)2 - 32 - 27 =

(x + 3)2 - 36 = 0

(x + 3)2 - 36 = 0 │+ 36

(x + 3)2 = 36 │√

│x + 3│= ± 6

x + 3 = ± 6 │- 3

x = - 3 ± 6

x₁ = 3

x₂ = - 9

Mats 11a / 0414 K05

b) x2 = 40 - 18x │- 40 + 18x

x2 + 18x - 40 = 0

QE: (18/2)2 = 92

x2 + 18x + 0 - 40 =

x2 + 18x + 92 - 92 - 40 = 0

x2 + 18x + 92 - 92 - 40 =

(x + 9)2 - 92 - 40 =

(x + 9)2 - 12.....[Volltext lesen]

x2- 12x + 62 - 62 - 28 = 0

x2- 12x + 62 - 62 - 28 =

(x - 6)2 - 62 - 28 =

(x - 6)2 - 64 = 0

(x - 6)2 - 64 = 0 │+ 64

(x - 6)2 = 64 │√

│x - 6│= ± 8

x - 6 = ± 8 │+ 6

x = 6 ± 8

x₁ = 14

x₂ = - 2

e) x (x + 34) = 35

x2+ 34x = 35 │- 35

x2 + 34x - 35 = 0

QE: (34/2)2 = 172

x2 + 34x + 0 - 35 =

x2 + 34x + 172 - 172 - 35 = 0

x2 + 34x + 172 - 172 - 35 =

(x + 17)2 - 172 - 35 =

(x + 17)2 - 324 = 0

(x + 17)2 - 324 = 0 │+ 324

(x + 17)2 = 324 │√

│x + 17│= ± 18

x + 17 = ± 18 │- 17

x = - 17 ± 18

x₁ = 1

x₂ = - 35

Mats 11a / 0414 K05

f) 47 + 46x = x2 │- x2

- x2 + 46x + 47 = 0 │- 47

- x2+ 46x =- 47 │: (- 1)

x2- 46x= 47

- x2+ 78x =160 │: (- 1)

x2- 78x= - 160

QE: (-78/2)2 = (-39)2

x2-78x + 0 = - 160

x2- 78x + (- 39)2= - (- 39)2- 160

x2- 78x + (- 39)2= - (- 39)2- 160

(x - 39)2=1.521 - 160

(x -39)2= 1361

(x -39)2 = 1361 │√

│x -39│= ± 36,892

x -39 = ± 36,892 │+39

x = 39 ± 36,892

x₁ = 2,108

x₂ = 75.....