2vsnijpunten kwadratische formules

Klas 2 vwo h7: snijpunten kwadratische formules en x2 = getal www.al-awwadi.nl

Klas 2 vwo h7: snijpunten kwadratische formules

Wat ga je leren:

• Snijpunten kwadratische formules• Ontbinden en oplossen• Verband tussen haakjes wegwerken en ontbinden• Alle soorten kwadratische vergelijkingen• Toepassingen van kwadratische formules

Klas 2 vwo h7: snijpunten kwadratische formules www.al-awwadi.nlOp1. Gegeven de formules y =x2 en y =−2x+3.

a) Teken de grafieken van de formules in één figuur.

b) Geef de coördinaten van de snijpunten



x -3 -2 -1 0 1 2 3

y


y =x2

y =−2x+3.

x 0 1 2

y



x -3 -2 -1 0 1 2 3

y 0


y =x2

y =−2x+3.

x 0 1 2

y



x -3 -2 -1 0 1 2 3

y 1 0 1


y =x2

y =−2x+3.

x 0 1 2

y



x -3 -2 -1 0 1 2 3

y 4 1 0 1 4


y =x2

y =−2x+3.

x 0 1 2

y



x -3 -2 -1 0 1 2 3

y 9 4 1 0 1 4 9


y =x2

y =−2x+3.

x 0 1 2

y



x -3 -2 -1 0 1 2 3

y 9 4 1 0 1 4 9


y =x2

y =−2x+3.

x 0 1 2

y 3



x -3 -2 -1 0 1 2 3

y 9 4 1 0 1 4 9


y =x2

y =−2x+3.

x 0 1 2

y 3 1



x -3 -2 -1 0 1 2 3

y 9 4 1 0 1 4 9


y =x2

y =−2x+3.

x 0 1 2

y 3 1 −1



x -3 -2 -1 0 1 2 3

y 9 4 1 0 1 4 9


y =x2

y =−2x+3.

x 0 1 2

y 3 1 −1

987654321

0-1

-6 -5 -4 -3 -2 -1 1 2 3 4

y

x

y =x2



x -3 -2 -1 0 1 2 3

y 9 4 1 0 1 4 9


y =x2

y =−2x+3.

x 0 1 2

y 3 1 −1

987654321

0-1

-6 -5 -4 -3 -2 -1 1 2 3 4

y

x

y =x2

y =−2x+3

A

B



x -3 -2 -1 0 1 2 3

y 9 4 1 0 1 4 9


y =x2

y =−2x+3.

x 0 1 2 −3

y 3 1 −1

987654321

0-1

-6 -5 -4 -3 -2 -1 1 2 3 4

y

x

y =x2

y =−2x+3

A

B



x -3 -2 -1 0 1 2 3

y 9 4 1 0 1 4 9


y =x2

y =−2x+3

x 0 1 2 −3

y 3 1 −1 9

987654321

0-1

-6 -5 -4 -3 -2 -1 1 2 3 4

y

x

y =x2

A

B

y =−2x+3

A(−3,9) en



x -3 -2 -1 0 1 2 3

y 9 4 1 0 1 4 9


y =x2

y =−2x+3

x 0 1 2 −3

y 3 1 −1 9

987654321

0-1

-6 -5 -4 -3 -2 -1 1 2 3 4

y

x

y =x2

A

B

y =−2x+3

A(−3,9) en B(1,1)


op 2. Geef de coördinaten van de snijpunten van y =0,5x2 en y =1,5x+2

987654321

0-1

-6 -5 -4 -3 -2 -1 1 2 3 4

x

y =0,5x2

B

y =−2x+3

y

y =1,5x+2



(−1; 0,5)

987654321

0-1

-6 -5 -4 -3 -2 -1 1 2 3 4

x

y =0,5x2

B

y =−2x+3

y

y =1,5x+2



(−1; 0,5) en (4,8)

987654321

0-1

-6 -5 -4 -3 -2 -1 1 2 3 4

x

y =0,5x2

B

y =−2x+3

y

y =1,5x+2



(−1; 0,5) en (4,8)

987654321

0-1

-6 -5 -4 -3 -2 -1 1 2 3 4

x

y =0,5x2

B

y

y =1,5x+2

op 3. Geef de coördinaten van de snijpunten van y =0,5x2 −3 en

a) y = -1

b) y = 5

c) y = -4

987654321

0-1

-2

-3

x

y =0,5x2 −3

B

y

-6 -5 -4 -3 -2 -1 1 2 3 4



(−1; 0,5) en (4,8)

987654321

0-1

-6 -5 -4 -3 -2 -1 1 2 3 4

x

y =0,5x2

B

y

y =1,5x+2


a) y = -1

b) y = 5

c) y = -4

987654321

0-1

-2

-3

x

y =0,5x2 −3

B

y

-6 -5 -4 -3 -2 -1 1 2 3 4

y = -1



(−1; 0,5) en (4,8)

987654321

0-1

-6 -5 -4 -3 -2 -1 1 2 3 4

x

y =0,5x2

B

y

y =1,5x+2


a) y = -1 snijpunten zijn (-2,-1) en (2,-1)

b) y = 5

c) y = -4

987654321

0-1

-2

-3

x

y =0,5x2 −3

B

y

-6 -5 -4 -3 -2 -1 1 2 3 4

y = -1



(−1; 0,5) en (4,8)

987654321

0-1a) y = 5

x

y =0,5x2

B

y

y =1,5x+2



b) y = 5

c) y = -4

987654321

0-1

-2

-3

x

y =0,5x2 −3

B

y

-6 -5 -4 -3 -2 -1 1 2 3 4

y = -1



(−1; 0,5) en (4,8)

987654321

0-1a) y = 5

x

y =0,5x2

B

y

y =1,5x+2



b) y = 5 snijpunten zijn (-4,5) en (4,5)

c) y = -4

987654321

0-1

-2

-3

-4

x

y =0,5x2 −3

B

y

-6 -5 -4 -3 -2 -1 1 2 3 4

y = -1



(−1; 0,5) en (4,8)

987654321

0-1a) y = 5

x

y =0,5x2

B

y

y =1,5x+2




c) y = -4

987654321

0-1

-2

-3

-4

x

y =0,5x2 −3

B

y

-6 -5 -4 -3 -2 -1 1 2 3 4

y = -1

y = -4



(−1; 0,5) en (4,8)

987654321

0-1a) y = 5

x

y =0,5x2

B

y

y =1,5x+2




c) y = -4 geen snijpunten

987654321

0-1

-2

-3

-4

x

y =0,5x2 −3

B

y

-6 -5 -4 -3 -2 -1 1 2 3 4

y = -1

y = -4


op 4. Geef oplossing van x2 =9

manier 1manier 2


op 4. Geef oplossing van x2 =9 manier 1

Maak een tekening en lees de x-snijpunt(en) afmanier 2

987654321

0-1

-6 -5 -4 -3 -2 -1 1 2 3 4

x

y =x2

y




987654321

0-1

-6 -5 -4 -3 -2 -1 1 2 3 4

x

y =x2

yy=9




987654321

0-1

-6 -5 -4 -3 -2 -1 1 2 3 4

x

y =x2

yy=9

oplossingen zijn dusx = -3 of x = 3



Maak een tekening en lees de x-snijpunt(en) afmanier 2:Oplossen zonder tekening, maar door worteltrekken. 9

87654321

0-1

-6 -5 -4 -3 -2 -1 1 2 3 4

x

y =x2

yy=9

oplossingen zijn dusx = 3 of x = −3



Maak een tekening en lees de x-snijpunt(en) afmanier 2:Oplossen zonder tekening, maar door worteltrekken.

x2 =9

987654321

0-1

-6 -5 -4 -3 -2 -1 1 2 3 4

x

y =x2

yy=9





x2 =9x =√9 of

987654321

0-1

-6 -5 -4 -3 -2 -1 1 2 3 4

x

y =x2

yy=9





x2 =9x =√9 of x =−√9

987654321

0-1

-6 -5 -4 -3 -2 -1 1 2 3 4

x

y =x2

yy=9





x2 =9x =√9 of x =−√9x = 3 of x = −3

987654321

0-1

-6 -5 -4 -3 -2 -1 1 2 3 4

x

y =x2

yy=9

oplossingen zijn dusx = 3 of x = -3



manier 1Maak een tekening en lees de x-snijpunt(en) af

manier 2:Oplossen zonder tekening, maar door worteltrekken.

x2 =9x =√9 of x =−√9x = 3 of x = −3

Op 5. Los op

987654321

0-1

-6 -5 -4 -3 -2 -1 1 2 3 4

x

y =x2

yy=9


Je ziet dat manier 2 veel beter werkt, dat gaan we voortaan toepassen.

a) x2 =49 c) x2 =10

c) x2 =0 d) x2 =−9





x2 =9x =√9 of x =−√9x = 3 of x = −3

Op 5. Los op

987654321

0-1

-6 -5 -4 -3 -2 -1 1 2 3 4

x

y =x2

yy=9



a) x2 =49 c) x2 =10x =√49 of x =−√49

c) x2 =0 d) x2 =−9





x2 =9x =√9 of x =−√9x = 3 of x = −3

Op 5. Los op

987654321

0-1

-6 -5 -4 -3 -2 -1 1 2 3 4

x

y =x2

yy=9



a) x2 =49 c) x2 =10x =√49 of x =−√49x =7 of x = −7

c) x2 =0 d) x2 =−9





x2 =9x =√9 of x =−√9x = 3 of x = −3

Op 5. Los op

987654321

0-1

-6 -5 -4 -3 -2 -1 1 2 3 4

x

y =x2

yy=9



a) x2 =49 c) x2 =10

x =√49 of x =−√49 x =√10 of x =−√10x =7 of x = −7

c) x2 =0 d) x2 =−9





x2 =9x =√9 of x =−√9x = 3 of x = −3

Op 5. Los op

987654321

0-1

-6 -5 -4 -3 -2 -1 1 2 3 4

x

y =x2

yy=9



a) x2 =49 c) x2 =10

x =√49 of x =−√49 x =√10 of x =−√10x =7 of x = −7

c) x2 =0 d) x2 =−9

x =√0 of x =−√0





x2 =9x =√9 of x =−√9x = 3 of x = −3

Op 5. Los op

987654321

0-1

-6 -5 -4 -3 -2 -1 1 2 3 4

x

y =x2

yy=9



a) x2 =49 c) x2 =10

x =√49 of x =−√49 x =√10 of x =−√10x =7 of x = −7

c) x2 =0 d) x2 =−9

x =√0 of x =−√0 x =0 of x =−0Dus eigenlijk x=0





x2 =9x =√9 of x =−√9x = 3 of x = −3

Op 5. Los op

987654321

0-1

-6 -5 -4 -3 -2 -1 1 2 3 4

x

y =x2

yy=9



a) x2 =49 c) x2 =10

x =√49 of x =−√49 x =√10 of x =−√10x =7 of x = −7

c) x2 =0 d) x2 =−9

x =√0 of x =−√0 wortel -9 kan niet x =0 of x =−0Dus eigenlijk x=0





x2 =9x =√9 of x =−√9x = 3 of x = −3

Op 5. Los op

987654321

0-1

-6 -5 -4 -3 -2 -1 1 2 3 4

x

y =x2

yy=9



a) x2 =49 c) x2 =10

x =√49 of x =−√49 x =√10 of x =−√10x =7 of x = −7

c) x2 =0 d) x2 =−9

x =√0 of x =−√0 wortel -9 kan niet x =0 of x =−0 dus geen oplossingDus eigenlijk x=0





x2 =9x =√9 of x =−√9x = 3 of x = −3

Op 5. Los op

987654321

0-1

-6 -5 -4 -3 -2 -1 1 2 3 4

x

y =x2

yy=9



a) x2 =49 c) x2 =10

x =√49 of x =−√49 x =√10 of x =−√10x =7 of x = −7

c) x2 =0 d) x2 =−9


Leerpunten:bij x2 = postitief getal





x2 =9x =√9 of x =−√9x = 3 of x = −3

Op 5. Los op

987654321

0-1

-6 -5 -4 -3 -2 -1 1 2 3 4

x

y =x2

yy=9



a) x2 =49 c) x2 =10

x =√49 of x =−√49 x =√10 of x =−√10x =7 of x = −72 oplossingen 2 oplossingen

c) x2 =0 d) x2 =−9


Leerpunten:bij x2 = postitief getal heb je 2 oplossingen





x2 =9x =√9 of x =−√9x = 3 of x = −3

Op 5. Los op

987654321

0-1

-6 -5 -4 -3 -2 -1 1 2 3 4

x

y =x2

yy=9



a) x2 =49 c) x2 =10


c) x2 =0 d) x2 =−9


Leerpunten:bij x2 = postitief getal heb je 2 oplossingenbij x2 = 0





x2 =9x =√9 of x =−√9x = 3 of x = −3

Op 5. Los op

987654321

0-1

-6 -5 -4 -3 -2 -1 1 2 3 4

x

y =x2

yy=9



a) x2 =49 c) x2 =10


c) x2 =0 d) x2 =−9


Leerpunten:bij x2 = postitief getal heb je 2 oplossingenbij x2 = 0 1 oplossing

1 oplossing





x2 =9x =√9 of x =−√9x = 3 of x = −3

Op 5. Los op

987654321

0-1

-6 -5 -4 -3 -2 -1 1 2 3 4

x

y =x2

yy=9



a) x2 =49 c) x2 =10


c) x2 =0 d) x2 =−9


Leerpunten:bij x2 = postitief getal heb je 2 oplossingenbij x2 = 0 1 oplossingbij x2 =negatief getal

1 oplossing





x2 =9x =√9 of x =−√9x = 3 of x = −3

Op 5. Los op

987654321

0-1

-6 -5 -4 -3 -2 -1 1 2 3 4

x

y =x2

yy=9



a) x2 =49 c) x2 =10


c) x2 =0 d) x2 =−9


Leerpunten:bij x2 = postitief getal heb je 2 oplossingenbij x2 = 0 1 oplossingbij x2 =negatief getal geen oplossing

1 oplossing

Klas 2 vwo h7: snijpunten kwadratische formules www.al-awwadi.nl

a) x2 =9 b)2x2 +1=3 c) ¾x2 = 12 d) 0,03x2 −2 = −2 e) -0,5x2 =18

op 1. Los op


a) x2 =9 b)2x2 +1=3 c) ¾x2 = 12 d) 0,03x2 −2 = −2 e) -0,5x2 =18

x =√9 v x =−√9

op 1. Los op


a) x2 =9 b)2x2 +1=3 c) ¾x2 = 12 d) 0,03x2 −2 = −2 e) -0,5x2 =18

x =√9 v x =−√9x = 3 v x = −3

op 1. Los op


a) x2 =9 b)2x2 +1= 3 c) ¾x2 = 12 d) 0,03x2 −2 = −2 e) -0,5x2 =18

x =√9 v x =−√9x = 3 v x = −3 2x2 = 2

op 1. Los op

−1 −1


a) x2 =9 b)2x2 +1= 3 c) ¾x2 = 12 d) 0,03x2 −2 = −2 e) -0,5x2 =18

x =√9 v x =−√9x = 3 v x = −3 2x2 = 2

:2 :2

op 1. Los op

−1 −1

x2 = 1


a) x2 =9 b)2x2 +1= 3 c) ¾x2 = 12 d) 0,03x2 −2 = −2 e) -0,5x2 =18

x =√9 v x =−√9x = 3 v x = −3 2x2 = 2

:2 :2

op 1. Los op

−1 −1

x2 = 1x =√1 v x =−√1

x = 1 v x = −1


a) x2 =9 b)2x2 +1= 3 c) ¾x2 = 12 d) 0,03x2 −2 = −2 e) -0,5x2 =18

x =√9 v x =−√9x = 3 v x = −3 2x2 = 2

:2 :2

op 1. Los op

−1 −1

x2 = 1x =√1 v x =−√1

x = 1 v x = −1

4 43x2 = 48


a) x2 =9 b)2x2 +1= 3 c) ¾x2 = 12 d) 0,03x2 −2 = −2 e) -0,5x2 =18

x =√9 v x =−√9x = 3 v x = −3 2x2 = 2

:2 :2

op 1. Los op

−1 −1

x2 = 1x =√1 v x =−√1

x = 1 v x = −1

4 43x2 = 48 :3 :3x2 = 16


a) x2 =9 b)2x2 +1= 3 c) ¾x2 = 12 d) 0,03x2 −2 = −2 e) -0,5x2 =18

x =√9 v x =−√9x = 3 v x = −3 2x2 = 2

:2 :2

op 1. Los op

−1 −1

x2 = 1x =√1 v x =−√1

x = 1 v x = −1

4 43x2 = 48 :3 :3x2 = 16x =√16 v x =−√16x = 4 v x = −4


a) x2 =9 b)2x2 +1= 3 c) ¾x2 = 12 d) 0,03x2 −2 = −2 e) -0,5x2 =18

x =√9 v x =−√9x = 3 v x = −3 2x2 = 2

:2 :2

op 1. Los op

−1 −1

x2 = 1x =√1 v x =−√1

x = 1 v x = −1

4 43x2 = 48 :3 :3x2 = 16x =√16 v x =−√16x = 4 v x = −4

+2 +2 0,03x2 = 0


a) x2 =9 b)2x2 +1= 3 c) ¾x2 = 12 d) 0,03x2 −2 = −2 e) -0,5x2 =18

x =√9 v x =−√9x = 3 v x = −3 2x2 = 2

:2 :2

op 1. Los op

−1 −1

x2 = 1x =√1 v x =−√1

x = 1 v x = −1

4 43x2 = 48 :3 :3x2 = 16x =√16 v x =−√16x = 4 v x = −4

+2 +2 0,03x2 = 0 :0,03 :0,03x2 = 0


a) x2 =9 b)2x2 +1= 3 c) ¾x2 = 12 d) 0,03x2 −2 = −2 e) -0,5x2 =18

x =√9 v x =−√9x = 3 v x = −3 2x2 = 2

:2 :2

op 1. Los op

−1 −1

x2 = 1x =√1 v x =−√1

x = 1 v x = −1

4 43x2 = 48 :3 :3x2 = 16x =√16 v x =−√16x = 4 v x = −4

+2 +2 0,03x2 = 0 :0,03 :0,03x2 = 0x =√0x=0


a) x2 =9 b)2x2 +1= 3 c) ¾x2 = 12 d) 0,03x2 −2 = −2 e) -0,5x2 =18

x =√9 v x =−√9

x = 3 v x = −3 2x2 = 2 :2 :2

op 1. Los op

−1 −1

x2 = 1x =√1 v x =−√1

x = 1 v x = −1

4 43x2 = 48 :3 :3x2 = 16x =√16 v x =−√16x = 4 v x = −4

+2 +2 0,03x2 = 0 :0,03 :0,03x2 = 0x =√0x=0

:-0,5 :-0,5 x2 = -36


a) x2 =9 b)2x2 +1= 3 c) ¾x2 = 12 d) 0,03x2 −2 = −2 e) -0,5x2 =18x =√9 v x =−√9

x = 3 v x = −3 2x2 = 2

:2 :2

op 1. Los op

−1 −1

x2 = 1x =√1 v x =−√1

x = 1 v x = −1

4 43x2 = 48 :3 :3x2 = 16x =√16 v x =−√16x = 4 v x = −4

+2 +2 0,03x2 = 0 :0,03 :0,03x2 = 0x =√0x=0

op 2. Los op (schaduw vergelijking)

a) (x+4)2 =9 b)2(x−5)2+1= 3 c) −0,3(x+1)2 = −1,2 d) ¼x2 −3 = −3

:-0,5 :-0,5 x2 = -36

Geen oplossing


a) x2 =9 b)2x2 +1= 3 c) ¾x2 = 12 d) 0,03x2 −2 = −2 e) -0,5x2 =18x =√9 v x =−√9

x = 3 v x = −3 2x2 = 2

:2 :2

op 1. Los op

−1 −1

x2 = 1x =√1 v x =−√1

x = 1 v x = −1

4 43x2 = 48 :3 :3x2 = 16x =√16 v x =−√16x = 4 v x = −4

+2 +2 0,03x2 = 0 :0,03 :0,03x2 = 0x =√0x=0


a) (x+4)2 =9 b)2(x−5)2+1= 3 c) −0,3(x+1)2 = −1,2 d) ¼x2 −3 = −3

x+4 =√9 v x+4 =−√9

:-0,5 :-0,5 x2 = -36

Geen oplossing


a) x2 =9 b)2x2 +1= 3 c) ¾x2 = 12 d) 0,03x2 −2 = −2 e) -0,5x2 =18x =√9 v x =−√9

x = 3 v x = −3 2x2 = 2

:2 :2

op 1. Los op

−1 −1

x2 = 1x =√1 v x =−√1

x = 1 v x = −1

4 43x2 = 48 :3 :3x2 = 16x =√16 v x =−√16x = 4 v x = −4

+2 +2 0,03x2 = 0 :0,03 :0,03x2 = 0x =√0x=0


a) (x+4)2 =9 b)2(x−5)2+1= 3 c) −0,3(x+1)2 = −1,2 d) ¼x2 −3 = −3

x+4 =√9 v x+4 =−√9x+4 = 3 v x+4 = −3

:-0,5 :-0,5 x2 = -36

Geen oplossing


a) x2 =9 b)2x2 +1= 3 c) ¾x2 = 12 d) 0,03x2 −2 = −2 e) -0,5x2 =18x =√9 v x =−√9

x = 3 v x = −3 2x2 = 2

:2 :2

op 1. Los op

−1 −1

x2 = 1x =√1 v x =−√1

x = 1 v x = −1

4 43x2 = 48 :3 :3x2 = 16x =√16 v x =−√16x = 4 v x = −4

+2 +2 0,03x2 = 0 :0,03 :0,03x2 = 0x =√0x=0


a) (x+4)2 =9 b)2(x−5)2+1= 3 c) −0,3(x+1)2 = −1,2 d) ¼x2 −3 = −3

x+4 =√9 v x+4 =−√9x+4 = 3 v x+4 = −3 −4 −4 −4 −4

x = −1 v x = −7

:-0,5 :-0,5 x2 = -36

Geen oplossing


a) x2 =9 b)2x2 +1= 3 c) ¾x2 = 12 d) 0,03x2 −2 = −2 e) -0,5x2 =18x =√9 v x =−√9

x = 3 v x = −3 2x2 = 2

:2 :2

op 1. Los op

−1 −1

x2 = 1x =√1 v x =−√1

x = 1 v x = −1

4 43x2 = 48 :3 :3x2 = 16x =√16 v x =−√16x = 4 v x = −4

+2 +2 0,03x2 = 0 :0,03 :0,03x2 = 0x =√0x=0


a) (x+4)2 =9 b)2(x−5)2+1= 3 c) −0,3(x+1)2 = −1,2 d) ¼x2 −3 = −3

x+4 =√9 v x+4 =−√9x+4 = 3 v x+4 = −3 −4 −4 −4 −4 x = −1 v x = −7

−1 −12(x−5)2 = 2

:-0,5 :-0,5 x2 = -36

Geen oplossing


a) x2 =9 b)2x2 +1= 3 c) ¾x2 = 12 d) 0,03x2 −2 = −2 e) -0,5x2 =18x =√9 v x =−√9

x = 3 v x = −3 2x2 = 2

:2 :2

op 1. Los op

−1 −1

x2 = 1x =√1 v x =−√1

x = 1 v x = −1

4 43x2 = 48 :3 :3x2 = 16x =√16 v x =−√16x = 4 v x = −4

+2 +2 0,03x2 = 0 :0,03 :0,03x2 = 0x =√0x=0


a) (x+4)2 =9 b)2(x−5)2+1= 3 c) −0,3(x+1)2 = −1,2 d) ¼x2 −3 = −3

x+4 =√9 v x+4 =−√9x+4 = 3 v x+4 = −3 −4 −4 −4 −4 x = −1 v x = −7

−1 −12(x−5)2 = 2:2 :2 (x−5)2 = 1

:-0,5 :-0,5 x2 = -36

Geen oplossing


a) x2 =9 b)2x2 +1= 3 c) ¾x2 = 12 d) 0,03x2 −2 = −2 e) -0,5x2 =18x =√9 v x =−√9

x = 3 v x = −3 2x2 = 2

:2 :2

op 1. Los op

−1 −1

x2 = 1x =√1 v x =−√1

x = 1 v x = −1

4 43x2 = 48 :3 :3x2 = 16x =√16 v x =−√16x = 4 v x = −4

+2 +2 0,03x2 = 0 :0,03 :0,03x2 = 0x =√0x=0


a) (x+4)2 =9 b)2(x−5)2+1= 3 c) −0,3(x+1)2 = −1,2 d) ¼x2 −3 = −3

x+4 =√9 v x+4 =−√9x+4 = 3 v x+4 = −3 −4 −4 −4 −4 x = −1 v x = −7

−1 −12(x−5)2 = 2:2 :2 (x−5)2 = 1 x−5 =√1 v x−5 =−√1

:-0,5 :-0,5 x2 = -36

Geen oplossing


a) x2 =9 b)2x2 +1= 3 c) ¾x2 = 12 d) 0,03x2 −2 = −2 e) -0,5x2 =18x =√9 v x =−√9

x = 3 v x = −3 2x2 = 2

:2 :2

op 1. Los op

−1 −1

x2 = 1x =√1 v x =−√1

x = 1 v x = −1

4 43x2 = 48 :3 :3x2 = 16x =√16 v x =−√16x = 4 v x = −4

+2 +2 0,03x2 = 0 :0,03 :0,03x2 = 0x =√0x=0


a) (x+4)2 =9 b)2(x−5)2+1= 3 c) −0,3(x+1)2 = −1,2 d) ¼x2 −3 = −3

x+4 =√9 v x+4 =−√9x+4 = 3 v x+4 = −3 −4 −4 −4 −4 x = −1 v x = −7

−1 −12(x−5)2 = 2:2 :2 (x−5)2 = 1 x−5 =√1 v x−5 =−√1

x−5 =1 v x−5 =−1

:-0,5 :-0,5 x2 = -36

Geen oplossing


a) x2 =9 b)2x2 +1= 3 c) ¾x2 = 12 d) 0,03x2 −2 = −2 e) -0,5x2 =18x =√9 v x =−√9

x = 3 v x = −3 2x2 = 2

:2 :2

op 1. Los op

−1 −1

x2 = 1x =√1 v x =−√1

x = 1 v x = −1

4 43x2 = 48 :3 :3x2 = 16x =√16 v x =−√16x = 4 v x = −4

+2 +2 0,03x2 = 0 :0,03 :0,03x2 = 0x =√0x=0


a) (x+4)2 =9 b)2(x−5)2+1= 3 c) −0,3(x+1)2 = −1,2 d) ¼x2 −3 = −3

x+4 =√9 v x+4 =−√9x+4 = 3 v x+4 = −3 −4 −4 −4 −4 x = −1 v x = −7

−1 −12(x−5)2 = 2:2 :2 (x−5)2 = 1 x−5 =√1 v x−5 =−√1

x−5 =1 v x−5 =−1 +5 +5 +5 +5x = 6 v x = 4

:-0,5 :-0,5 x2 = -36

Geen oplossing


a) x2 =9 b)2x2 +1= 3 c) ¾x2 = 12 d) 0,03x2 −2 = −2 e) -0,5x2 =18x =√9 v x =−√9

x = 3 v x = −3 2x2 = 2

:2 :2

op 1. Los op

−1 −1

x2 = 1x =√1 v x =−√1

x = 1 v x = −1

4 43x2 = 48 :3 :3x2 = 16x =√16 v x =−√16x = 4 v x = −4

+2 +2 0,03x2 = 0 :0,03 :0,03x2 = 0x =√0x=0


a) (x+4)2 =9 b)2(x−5)2+1= 3 c) −0,3(x+1)2 = −1,2 d) ¼x2 −3 = −3

x+4 =√9 v x+4 =−√9x+4 = 3 v x+4 = −3 −4 −4 −4 −4 x = −1 v x = −7

−1 −12(x−5)2 = 2:2 :2 (x−5)2 = 1 x−5 =√1 v x−5 =−√1

x−5 =1 v x−5 =−1 +5 +5 +5 +5x = 6 v x = 4

:−0,3 :−0,3(x+1)2 = 4

:-0,5 :-0,5 x2 = -36

Geen oplossing


a) x2 =9 b)2x2 +1= 3 c) ¾x2 = 12 d) 0,03x2 −2 = −2 e) -0,5x2 =18x =√9 v x =−√9

x = 3 v x = −3 2x2 = 2

:2 :2

op 1. Los op

−1 −1

x2 = 1x =√1 v x =−√1

x = 1 v x = −1

4 43x2 = 48 :3 :3x2 = 16x =√16 v x =−√16x = 4 v x = −4

+2 +2 0,03x2 = 0 :0,03 :0,03x2 = 0x =√0x=0


a) (x+4)2 =9 b)2(x−5)2+1= 3 c) −0,3(x+1)2 = −1,2 d) ¼x2 −3 = −3

x+4 =√9 v x+4 =−√9x+4 = 3 v x+4 = −3 −4 −4 −4 −4 x = −1 v x = −7

−1 −12(x−5)2 = 2:2 :2 (x−5)2 = 1 x−5 =√1 v x−5 =−√1

x−5 =1 v x−5 =−1 +5 +5 +5 +5x = 6 v x = 4

:−0,3 :−0,3(x+1)2 = 4

x +1 = √4 v x +1 = −√4

:-0,5 :-0,5 x2 = -36

Geen oplossing


a) x2 =9 b)2x2 +1= 3 c) ¾x2 = 12 d) 0,03x2 −2 = −2 e) -0,5x2 =18x =√9 v x =−√9

x = 3 v x = −3 2x2 = 2

:2 :2

op 1. Los op

−1 −1

x2 = 1x =√1 v x =−√1

x = 1 v x = −1

4 43x2 = 48 :3 :3x2 = 16x =√16 v x =−√16x = 4 v x = −4

+2 +2 0,03x2 = 0 :0,03 :0,03x2 = 0x =√0x=0


a) (x+4)2 =9 b)2(x−5)2+1= 3 c) −0,3(x+1)2 = −1,2 d) ¼x2 −3 = −3

x+4 =√9 v x+4 =−√9x+4 = 3 v x+4 = −3 −4 −4 −4 −4 x = −1 v x = −7

−1 −12(x−5)2 = 2:2 :2 (x−5)2 = 1 x−5 =√1 v x−5 =−√1

x−5 =1 v x−5 =−1 +5 +5 +5 +5x = 6 v x = 4

:−0,3 :−0,3(x+1)2 = 4

x +1 = √4 v x +1 = −√4x +1 = 2 v x +1 = −2

:-0,5 :-0,5 x2 = -36

Geen oplossing


a) x2 =9 b)2x2 +1= 3 c) ¾x2 = 12 d) 0,03x2 −2 = −2 e) -0,5x2 =18x =√9 v x =−√9

x = 3 v x = −3 2x2 = 2

:2 :2

op 1. Los op

−1 −1

x2 = 1x =√1 v x =−√1

x = 1 v x = −1

4 43x2 = 48 :3 :3x2 = 16x =√16 v x =−√16x = 4 v x = −4

+2 +2 0,03x2 = 0 :0,03 :0,03x2 = 0x =√0x=0


a) (x+4)2 =9 b)2(x−5)2+1= 3 c) −0,3(x+1)2 = −1,2 d) ¼x2 −3 = −3

x+4 =√9 v x+4 =−√9x+4 = 3 v x+4 = −3 −4 −4 −4 −4 x = −1 v x = −7

−1 −12(x−5)2 = 2:2 :2 (x−5)2 = 1 x−5 =√1 v x−5 =−√1

x−5 =1 v x−5 =−1 +5 +5 +5 +5x = 6 v x = 4

:−0,3 :−0,3(x+1)2 = 4

x +1 = √4 v x +1 = −√4x +1 = 2 v x +1 = −2 −1 −1 −1 −1

:-0,5 :-0,5 x2 = -36

Geen oplossing


a) x2 =9 b)2x2 +1= 3 c) ¾x2 = 12 d) 0,03x2 −2 = −2 e) -0,5x2 =18x =√9 v x =−√9

x = 3 v x = −3 2x2 = 2

:2 :2

op 1. Los op

−1 −1

x2 = 1x =√1 v x =−√1

x = 1 v x = −1

4 43x2 = 48 :3 :3x2 = 16x =√16 v x =−√16x = 4 v x = −4

+2 +2 0,03x2 = 0 :0,03 :0,03x2 = 0x =√0x=0


a) (x+4)2 =9 b)2(x−5)2+1= 3 c) −0,3(x+1)2 = −1,2 d) ¼x2 −3 = −3

x+4 =√9 v x+4 =−√9x+4 = 3 v x+4 = −3 −4 −4 −4 −4 x = −1 v x = −7

−1 −12(x−5)2 = 2:2 :2 (x−5)2 = 1 x−5 =√1 v x−5 =−√1

x−5 =1 v x−5 =−1 +5 +5 +5 +5x = 6 v x = 4

:−0,3 :−0,3(x+1)2 = 4

x +1 = √4 v x +1 = −√4x +1 = 2 v x +1 = −2 −1 −1 −1 −1x =1 v x=−3

:-0,5 :-0,5 x2 = -36

Geen oplossing

2vsnijpunten kwadratische formules

Documents