1
a

x 2 = x
x 2 x = 0
x ( x 1 ) = 0
x = 0    of    x = 1
Snijpunten: ( 0,0 ) en ( 1,1 )

b

x 2 = x + 2
x 2 x 2 = 0
( x 2 ) ( x + 1 ) = 0
x = 2    of    x = 1
Snijpunten: ( 2,4 ) en ( 1,1 )

c

x 2 = x 2
x 2 x + 2 = 0
a = 1 b = 1 c = 2 D = 1 4 1 2 = 7
D < 0 , dus geen snijpunten

d

-

e

x 2 = x 1
x 2 x + 1 = 0
a = 1 b = 1 c = 1 D = 1 4 1 1 = 3


x 2 = x
x 2 x = 0
a = 1 b = 1 c = 0 D = 1 4 1 0 = 1


x 2 = x + 1
x 2 x 1 = 0
a = 1 b = 1 c = 1 D = 1 4 1 1 = 5

f

x 2 x k = 0
a = 1 b = 1 c = k D = 1 4 1 k = 1 + 4 k

g

1 + 4 k = 0
4 k = 1
k = 1 4

h

x 2 = x 1 4
x 2 x + 1 4 = 0
x = b 2 a = 1 2 = 1 2 y = ( 1 2 ) 2 = 1 4
Raakpunt is ( 1 2 , 1 4 ) .

2
a

( 0,3 )

b

x 2 + 1 = a x + 3
x 2 + a x + 2 = 0

c

x 2 + a x + 2 = 0
a = 1 b = a c = 2 D = a 2 4 1 2 = a 2 8

d

Raken, dus D = 0 .
a 2 8 = 0
a 2 = 8
a = 8 = 2 2    of    a = 8 = 2 2

e

x 2 + 2 2 x + 2 = 0
x = 2 2 2 = 2 y = ( 2 ) 2 + 1 = 1
Raakpunt is ( 2 , 1 ) .

x 2 2 2 x + 2 = 0
x = 2 2 2 = 2 y = ( 2 ) 2 + 1 = 1
Raakpunt is ( 2 , 1 ) .

3
a

x 2 + 5 x + 4 = 0
( x + 1 ) ( x + 4 ) = 0
x = 1    of    x = 4

b

x 2 + k x + 4 = 0
a = 1 b = k c = 4 D = k 2 4 1 4 = k 2 16
Eén oplossing, dus D = 0 .
k 2 16 = 0
k 2 = 16
k = 4    of    k = 4

c

x 2 + 4 x + 4 = 0
( x + 2 ) 2 = 0
x = 2

4
a

p = 0 , want dan heb je een rechte lijn

b

p x 2 6 x 1 = 0
a = p b = 6 c = 1 D = 36 4 p 1 = 36 + 4 p
Eén raakpunt met x -as D = 0
36 + 4 p = 0
4 p = 36
p = 9

c

1 2 x 2 p x + 2 = 0
a = 1 2 b = p c = 2 D = ( p ) 2 4 1 2 2 = p 2 4
Twee snijpunten met x -as D > 0
p 2 4 > 0
p 2 > 4
p < 2    of    p > 2

d

2 x 2 + 4 x + p = 0
a = 2 b = 4 c = p D = 16 4 2 p = 16 8 p
Geen snij- of raakpunten punten met x -as D < 0
16 8 p < 0
16 < 8 p
2 < p

5
a

Omdat 0 = k 0 klopt, wat je ook voor k neemt.

b

Als k = 0 , dan y = 0 ; 5 = k 2 k = 2 1 2

c

De verticale lijn door de oorsprong, dus de y -as

d

-

e

( x 1 ) 2 = k x
x 2 2 x + 1 = k x
x 2 2 x k x + 1 = 0
x 2 ( 2 + k ) x + 1 = 0

f

D = ( 2 + k ) 2 4 1 1 = ( 2 + k ) 2 4

g

Als k = 1 , dan D = 9 4 = 5 , dus twee snijpunten.

h

( 2 + k ) 2 4 = 0
( 2 + k ) 2 = 4
2 + k = 2    of    2 + k = 2
k = 0    of    k = 4

i

y = 0 en y = 4 x

6
a

4 x 2 = k x + 5
0 = x 2 + k x + 1
a = 1 b = k c = 1 D = k 2 4
Raaklijn als D = 0 k 2 4 = 0 k 2 = 4 k = 2 of k = 2

b

tan ( hellingshoek ) = 2 hellingshoek = 63 ° ;
tan ( hellingshoek ) = 2 hellingshoek = 63 ° , dus 180 ° 63 ° = 117 °