ABC-formule

Pak je Ipad en aantekeningenschrift

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Slide 1: Slide

WiskundeMiddelbare schoolvwoLeerjaar 2

This lesson contains 54 slides, with interactive quizzes and text slides.

Items in this lesson

ABC-formule

Pak je Ipad en aantekeningenschrift

Slide 1 - Slide

Opbouw

Uitleg 30 min

Zelfstandig werken 20 min

(Uitleg 15 min)

Zelfstandig werken 15 min

Afsluiting 10 min

Slide 2 - Slide

Kwadratische vergelijkingen

--> wortel nemen

--> haakjes maken

x^{​ 2 ​ ​} = 81

3 x^{​ 2 ​ ​} + 12 x = 0

Slide 3 - Slide

Kwadratische vergelijkingen

--> wortel nemen

--> haakjes maken

--> ?

x^{​ 2 ​ ​} = 81

3 x^{​ 2 ​ ​} + 12 x = 0

7 x^{​ 2 ​ ​} + 9 x - 12 = 0

Slide 4 - Slide

Leerdoelen

Je weet wat de a, b en c in een kwadratische formule zijn
Je kan een drieterm oplossen met de abc-formule
Je weet wat het verschil tussen een één-term, twee-term en drie-term vergelijking is
Je kan de juiste oplossingmethode bij een kwadratische vergelijking kiezen

Slide 5 - Slide

Drietermen oplossen

19 x^{​ 2 ​ ​} + x - 3 = 0

5 x^{​ 2 ​ ​} + 9 x + 12 = 0

6 x^{​ 2 ​ ​} - 7 x + 1 = 0

Slide 6 - Slide

Drietermen oplossen

19 x^{​ 2 ​ ​} + x - 3 = 0

5 x^{​ 2 ​ ​} + 9 x + 12 = 0

6 x^{​ 2 ​ ​} - 7 x + 1 = 0

a x^{​ 2 ​ ​} + b x + c = 0

Slide 7 - Slide

Drietermen oplossen

19 x^{​ 2 ​ ​} + x - 3 = 0

5 x^{​ 2 ​ ​} + 9 x + 12 = 0

6 x^{​ 2 ​ ​} - 7 x + 1 = 0

a x^{​ 2 ​ ​} + b x + c = 0

a = 5

Slide 8 - Slide

Drietermen oplossen

19 x^{​ 2 ​ ​} + x - 3 = 0

5 x^{​ 2 ​ ​} + 9 x + 12 = 0

6 x^{​ 2 ​ ​} - 7 x + 1 = 0

a x^{​ 2 ​ ​} + b x + c = 0

a = 5

b = 9

Slide 9 - Slide

Drietermen oplossen

19 x^{​ 2 ​ ​} + x - 3 = 0

5 x^{​ 2 ​ ​} + 9 x + 12 = 0

6 x^{​ 2 ​ ​} - 7 x + 1 = 0

a x^{​ 2 ​ ​} + b x + c = 0

a = 5

b = 9

c = 12

Slide 10 - Slide

Drietermen oplossen

19 x^{​ 2 ​ ​} + x - 3 = 0

5 x^{​ 2 ​ ​} + 9 x + 12 = 0

6 x^{​ 2 ​ ​} - 7 x + 1 = 0

a x^{​ 2 ​ ​} + b x + c = 0

a = 5

b = 9

c = 12

a = 19

Slide 11 - Slide

Drietermen oplossen

19 x^{​ 2 ​ ​} + x - 3 = 0

5 x^{​ 2 ​ ​} + 9 x + 12 = 0

6 x^{​ 2 ​ ​} - 7 x + 1 = 0

a x^{​ 2 ​ ​} + b x + c = 0

a = 5

b = 9

c = 12

a = 19

b = 1

Slide 12 - Slide

Drietermen oplossen

19 x^{​ 2 ​ ​} + x - 3 = 0

5 x^{​ 2 ​ ​} + 9 x + 12 = 0

6 x^{​ 2 ​ ​} - 7 x + 1 = 0

a x^{​ 2 ​ ​} + b x + c = 0

a = 5

b = 9

c = 12

a = 19

b = 1

c = - 3

Slide 13 - Slide

Drietermen oplossen

19 x^{​ 2 ​ ​} + x - 3 = 0

5 x^{​ 2 ​ ​} + 9 x + 12 = 0

6 x^{​ 2 ​ ​} - 7 x + 1 = 0

a x^{​ 2 ​ ​} + b x + c = 0

a = 5

b = 9

c = 12

a = 19

b = 1

c = - 3

a = 6

Slide 14 - Slide

Drietermen oplossen

19 x^{​ 2 ​ ​} + x - 3 = 0

5 x^{​ 2 ​ ​} + 9 x + 12 = 0

6 x^{​ 2 ​ ​} - 7 x + 1 = 0

a x^{​ 2 ​ ​} + b x + c = 0

a = 5

b = 9

c = 12

a = 19

b = 1

c = - 3

a = 6

b = - 7

Slide 15 - Slide

Drietermen oplossen

19 x^{​ 2 ​ ​} + x - 3 = 0

5 x^{​ 2 ​ ​} + 9 x + 12 = 0

6 x^{​ 2 ​ ​} - 7 x + 1 = 0

a x^{​ 2 ​ ​} + b x + c = 0

a = 5

b = 9

c = 12

a = 19

b = 1

c = - 3

a = 6

b = - 7

c = 1

Slide 16 - Slide

a = ..., b = ..., c = ...

3 x^{​ 2 ​ ​} + 2 x + 7 = 0

timer

1:00

Slide 17 - Open question

a = ..., b = ..., c = ...

3 x^{​ 2 ​ ​} + 2 x + 7 = 0

Slide 18 - Slide

a = 3, b = 2, c = 7

3 x^{​ 2 ​ ​} + 2 x + 7 = 0

Slide 19 - Slide

a = ..., b = ..., c = ...

8 x^{​ 2 ​ ​} + x - 3 = 0

timer

1:00

Slide 20 - Open question

a = ..., b = ..., c = ...

8 x^{​ 2 ​ ​} + x - 3 = 0

Slide 21 - Slide

a = 8, b = 1, c =-3

8 x^{​ 2 ​ ​} + x - 3 = 0

Slide 22 - Slide

a = 8, b = 1, c =-3

8 x^{​ 2 ​ ​} + x - 3 = 0

x = \frac{​ - b \pm \sqrt ​ b ^{​ 2 ​ ​} - 4 a c ​ ​ ​ ​ ​}{​ 2 a ​}

Slide 23 - Slide

Drieterm oplossen

3 x^{​ 2 ​ ​} + 18 x + 15 = 0

Slide 24 - Slide

Drieterm oplossen

3 x^{​ 2 ​ ​} + 18 x + 15 = 0

a = 3

b = 18

c = 15

Slide 25 - Slide

Drieterm oplossen

3 x^{​ 2 ​ ​} + 18 x + 15 = 0

a = 3

b = 18

c = 15

x = \frac{​ - b \pm \sqrt ​ b ^{​ 2 ​ ​} - 4 a c ​ ​ ​ ​ ​}{​ 2 a ​}

Slide 26 - Slide

Drieterm oplossen

3 x^{​ 2 ​ ​} + 18 x + 15 = 0

a = 3

b = 18

c = 15

x = \frac{​ - b \pm \sqrt ​ b ^{​ 2 ​ ​} - 4 a c ​ ​ ​ ​ ​}{​ 2 a ​}

x = \frac{​ - b \pm \sqrt ​ b ^{​ 2 ​ ​} - 4 \cdot 3 \cdot c ​ ​ ​ ​ ​}{​ 2 \cdot 3 ​}

Slide 27 - Slide

Drieterm oplossen

3 x^{​ 2 ​ ​} + 18 x + 15 = 0

a = 3

b = 18

c = 15

x = \frac{​ - b \pm \sqrt ​ b ^{​ 2 ​ ​} - 4 a c ​ ​ ​ ​ ​}{​ 2 a ​}

x = \frac{​ - 1 8 \pm \sqrt ​ ( 1 8 ) ^{​ 2 ​ ​} - 4 \cdot 3 \cdot c ​ ​ ​ ​ ​}{​ 2 \cdot 3 ​}

Slide 28 - Slide

Drieterm oplossen

3 x^{​ 2 ​ ​} + 18 x + 15 = 0

a = 3

b = 18

c = 15

x = \frac{​ - b \pm \sqrt ​ b ^{​ 2 ​ ​} - 4 a c ​ ​ ​ ​ ​}{​ 2 a ​}

x = \frac{​ - 1 8 \pm \sqrt ​ ( 1 8 ) ^{​ 2 ​ ​} - 4 \cdot 3 \cdot 1 5 ​ ​ ​ ​ ​}{​ 2 \cdot 3 ​}

Slide 29 - Slide

Drieterm oplossen

3 x^{​ 2 ​ ​} + 18 x + 15 = 0

a = 3

b = 18

c = 15

x = \frac{​ - b \pm \sqrt ​ b ^{​ 2 ​ ​} - 4 a c ​ ​ ​ ​ ​}{​ 2 a ​}

x = \frac{​ - 1 8 \pm \sqrt ​ 1 8 ^{​ 2 ​ ​} - 4 \cdot 3 \cdot 1 5 ​ ​ ​ ​ ​}{​ 2 \cdot 3 ​}

x = \frac{​ - 1 8 \pm \sqrt ​ ( 1 8 ) ^{​ 2 ​ ​} - 4 \cdot 3 \cdot 1 5 ​ ​ ​ ​ ​}{​ 2 \cdot 3 ​}

Slide 30 - Slide

Drieterm oplossen

3 x^{​ 2 ​ ​} + 18 x + 15 = 0

a = 3

b = 18

c = 15

x = \frac{​ - b \pm \sqrt ​ b ^{​ 2 ​ ​} - 4 a c ​ ​ ​ ​ ​}{​ 2 a ​}

x = \frac{​ - 1 8 \pm \sqrt ​ 1 8 ^{​ 2 ​ ​} - 4 \cdot 3 \cdot 1 5 ​ ​ ​ ​ ​}{​ 2 \cdot 3 ​}

x = \frac{​ - 1 8 \pm \sqrt ​ 3 2 4 - 1 8 0 ​ ​ ​ ​ ​}{​ 6 ​}

x = \frac{​ - 1 8 \pm \sqrt ​ ( 1 8 ) ^{​ 2 ​ ​} - 4 \cdot 3 \cdot 1 5 ​ ​ ​ ​ ​}{​ 2 \cdot 3 ​}

Slide 31 - Slide

Drieterm oplossen

3 x^{​ 2 ​ ​} + 18 x + 15 = 0

a = 3

b = 18

c = 15

x = \frac{​ - b \pm \sqrt ​ b ^{​ 2 ​ ​} - 4 a c ​ ​ ​ ​ ​}{​ 2 a ​}

x = \frac{​ - 1 8 \pm \sqrt ​ 1 8 ^{​ 2 ​ ​} - 4 \cdot 3 \cdot 1 5 ​ ​ ​ ​ ​}{​ 2 \cdot 3 ​}

x = \frac{​ - 1 8 \pm \sqrt ​ 3 2 4 - 1 8 0 ​ ​ ​ ​ ​}{​ 6 ​}

x = \frac{​ - 1 8 \pm \sqrt ​ 1 4 4 ​ ​ ​ ​ ​}{​ 6 ​}

x = \frac{​ - 1 8 \pm \sqrt ​ ( 1 8 ) ^{​ 2 ​ ​} - 4 \cdot 3 \cdot 1 5 ​ ​ ​ ​ ​}{​ 2 \cdot 3 ​}

Slide 32 - Slide

Drieterm oplossen

3 x^{​ 2 ​ ​} + 18 x + 15 = 0

a = 3

b = 18

c = 15

x = \frac{​ - b \pm \sqrt ​ b ^{​ 2 ​ ​} - 4 a c ​ ​ ​ ​ ​}{​ 2 a ​}

x = \frac{​ - 1 8 \pm \sqrt ​ 1 8 ^{​ 2 ​ ​} - 4 \cdot 3 \cdot 1 5 ​ ​ ​ ​ ​}{​ 2 \cdot 3 ​}

x = \frac{​ - 1 8 \pm \sqrt ​ 3 2 4 - 1 8 0 ​ ​ ​ ​ ​}{​ 6 ​}

x = \frac{​ - 1 8 \pm \sqrt ​ 1 4 4 ​ ​ ​ ​ ​}{​ 6 ​}

x = \frac{​ - 1 8 \pm \sqrt ​ ( 1 8 ) ^{​ 2 ​ ​} - 4 \cdot 3 \cdot 1 5 ​ ​ ​ ​ ​}{​ 2 \cdot 3 ​}

x = \frac{​ - 1 8 \pm 1 2 ​ ​}{​ 6 ​}

Slide 33 - Slide

Drieterm oplossen

3 x^{​ 2 ​ ​} + 18 x + 15 = 0

a = 3

b = 18

c = 15

x = \frac{​ - b \pm \sqrt ​ b ^{​ 2 ​ ​} - 4 a c ​ ​ ​ ​ ​}{​ 2 a ​}

x = \frac{​ - 1 8 \pm \sqrt ​ 1 8 ^{​ 2 ​ ​} - 4 \cdot 3 \cdot 1 5 ​ ​ ​ ​ ​}{​ 2 \cdot 3 ​}

x = \frac{​ - 1 8 \pm \sqrt ​ 3 2 4 - 1 8 0 ​ ​ ​ ​ ​}{​ 6 ​}

x = \frac{​ - 1 8 \pm \sqrt ​ 1 4 4 ​ ​ ​ ​ ​}{​ 6 ​}

x = \frac{​ - 1 8 \pm \sqrt ​ ( 1 8 ) ^{​ 2 ​ ​} - 4 \cdot 3 \cdot 1 5 ​ ​ ​ ​ ​}{​ 2 \cdot 3 ​}

x = \frac{​ - 1 8 \pm 1 2 ​ ​}{​ 6 ​}

x = \frac{​ - 1 8 + 1 2 ​ ​}{​ 6 ​}

x = \frac{​ - 1 8 - 1 2 ​ ​}{​ 6 ​}

Slide 34 - Slide

Drieterm oplossen

3 x^{​ 2 ​ ​} + 18 x + 15 = 0

a = 3

b = 18

c = 15

x = \frac{​ - b \pm \sqrt ​ b ^{​ 2 ​ ​} - 4 a c ​ ​ ​ ​ ​}{​ 2 a ​}

x = \frac{​ - 1 8 \pm \sqrt ​ 1 8 ^{​ 2 ​ ​} - 4 \cdot 3 \cdot 1 5 ​ ​ ​ ​ ​}{​ 2 \cdot 3 ​}

x = \frac{​ - 1 8 \pm \sqrt ​ 3 2 4 - 1 8 0 ​ ​ ​ ​ ​}{​ 6 ​}

x = \frac{​ - 1 8 \pm \sqrt ​ 1 4 4 ​ ​ ​ ​ ​}{​ 6 ​}

x = \frac{​ - 1 8 \pm \sqrt ​ ( 1 8 ) ^{​ 2 ​ ​} - 4 \cdot 3 \cdot 1 5 ​ ​ ​ ​ ​}{​ 2 \cdot 3 ​}

x = \frac{​ - 1 8 \pm 1 2 ​ ​}{​ 6 ​}

x = \frac{​ - 1 8 + 1 2 ​ ​}{​ 6 ​}

x = \frac{​ - 1 8 - 1 2 ​ ​}{​ 6 ​}

x = \frac{​ - 6 ​ ​}{​ 6 ​}

Slide 35 - Slide

Drieterm oplossen

3 x^{​ 2 ​ ​} + 18 x + 15 = 0

a = 3

b = 18

c = 15

x = \frac{​ - b \pm \sqrt ​ b ^{​ 2 ​ ​} - 4 a c ​ ​ ​ ​ ​}{​ 2 a ​}

x = \frac{​ - 1 8 \pm \sqrt ​ 1 8 ^{​ 2 ​ ​} - 4 \cdot 3 \cdot 1 5 ​ ​ ​ ​ ​}{​ 2 \cdot 3 ​}

x = \frac{​ - 1 8 \pm \sqrt ​ 3 2 4 - 1 8 0 ​ ​ ​ ​ ​}{​ 6 ​}

x = \frac{​ - 1 8 \pm \sqrt ​ 1 4 4 ​ ​ ​ ​ ​}{​ 6 ​}

x = \frac{​ - 1 8 \pm \sqrt ​ ( 1 8 ) ^{​ 2 ​ ​} - 4 \cdot 3 \cdot 1 5 ​ ​ ​ ​ ​}{​ 2 \cdot 3 ​}

x = \frac{​ - 1 8 \pm 1 2 ​ ​}{​ 6 ​}

x = \frac{​ - 1 8 + 1 2 ​ ​}{​ 6 ​}

x = \frac{​ - 1 8 - 1 2 ​ ​}{​ 6 ​}

x = \frac{​ - 6 ​ ​}{​ 6 ​}

x = \frac{​ - 3 0 ​ ​}{​ 6 ​}

Slide 36 - Slide

Drieterm oplossen

3 x^{​ 2 ​ ​} + 18 x + 15 = 0

a = 3

b = 18

c = 15

x = \frac{​ - b \pm \sqrt ​ b ^{​ 2 ​ ​} - 4 a c ​ ​ ​ ​ ​}{​ 2 a ​}

x = \frac{​ - 1 8 \pm \sqrt ​ 1 8 ^{​ 2 ​ ​} - 4 \cdot 3 \cdot 1 5 ​ ​ ​ ​ ​}{​ 2 \cdot 3 ​}

x = \frac{​ - 1 8 \pm \sqrt ​ 3 2 4 - 1 8 0 ​ ​ ​ ​ ​}{​ 6 ​}

x = \frac{​ - 1 8 \pm \sqrt ​ 1 4 4 ​ ​ ​ ​ ​}{​ 6 ​}

x = \frac{​ - 1 8 \pm \sqrt ​ ( 1 8 ) ^{​ 2 ​ ​} - 4 \cdot 3 \cdot 1 5 ​ ​ ​ ​ ​}{​ 2 \cdot 3 ​}

x = \frac{​ - 1 8 \pm 1 2 ​ ​}{​ 6 ​}

x = \frac{​ - 1 8 + 1 2 ​ ​}{​ 6 ​}

x = \frac{​ - 1 8 - 1 2 ​ ​}{​ 6 ​}

x = \frac{​ - 6 ​ ​}{​ 6 ​}

x = \frac{​ - 3 0 ​ ​}{​ 6 ​}

x = - 1

Slide 37 - Slide

Drieterm oplossen

3 x^{​ 2 ​ ​} + 18 x + 15 = 0

a = 3

b = 18

c = 15

x = \frac{​ - b \pm \sqrt ​ b ^{​ 2 ​ ​} - 4 a c ​ ​ ​ ​ ​}{​ 2 a ​}

x = \frac{​ - 1 8 \pm \sqrt ​ 1 8 ^{​ 2 ​ ​} - 4 \cdot 3 \cdot 1 5 ​ ​ ​ ​ ​}{​ 2 \cdot 3 ​}

x = \frac{​ - 1 8 \pm \sqrt ​ 3 2 4 - 1 8 0 ​ ​ ​ ​ ​}{​ 6 ​}

x = \frac{​ - 1 8 \pm \sqrt ​ 1 4 4 ​ ​ ​ ​ ​}{​ 6 ​}

x = \frac{​ - 1 8 \pm \sqrt ​ ( 1 8 ) ^{​ 2 ​ ​} - 4 \cdot 3 \cdot 1 5 ​ ​ ​ ​ ​}{​ 2 \cdot 3 ​}

x = \frac{​ - 1 8 \pm 1 2 ​ ​}{​ 6 ​}

x = \frac{​ - 1 8 + 1 2 ​ ​}{​ 6 ​}

x = \frac{​ - 1 8 - 1 2 ​ ​}{​ 6 ​}

x = \frac{​ - 6 ​ ​}{​ 6 ​}

x = \frac{​ - 3 0 ​ ​}{​ 6 ​}

x = - 1

x = - 5

Slide 38 - Slide

Aantekening: 8.6 Drieterm oplossen

Stappenplan:

1. Zorg voor = 0

2. Schrijf de a, b en c op

3. Schrijf de abc-formule op

4. Vul de abc-formule in

5. Bereken de oplossingen

Slide 39 - Slide

Aantekening: Voorbeeld

2 x^{​ 2 ​ ​} - 24 x + 64 = 0

Slide 40 - Slide

Drieterm oplossen

- 5 x^{​ 2 ​ ​} - 15 x + 90 = 0

Slide 41 - Slide

Drieterm oplossen

- 5 x^{​ 2 ​ ​} - 15 x + 90 = 0

a = - 5

b = - 15

c = 90

Slide 42 - Slide

Drieterm oplossen

- 5 x^{​ 2 ​ ​} - 15 x + 90 = 0

a = - 5

b = - 15

c = 90

x = \frac{​ - b \pm \sqrt ​ b ^{​ 2 ​ ​} - 4 a c ​ ​ ​ ​ ​}{​ 2 a ​}

Slide 43 - Slide

Drieterm oplossen

- 5 x^{​ 2 ​ ​} - 15 x + 90 = 0

a = - 5

b = - 15

c = 90

x = \frac{​ - b \pm \sqrt ​ b ^{​ 2 ​ ​} - 4 a c ​ ​ ​ ​ ​}{​ 2 a ​}

x = \frac{​ - - 1 5 \pm \sqrt ​ ( - 1 5 ) ^{​ 2 ​ ​} - 4 \cdot - 5 \cdot 9 0 ​ ​ ​ ​ ​}{​ 2 \cdot - 5 ​}

Slide 44 - Slide

Drieterm oplossen

- 5 x^{​ 2 ​ ​} - 15 x + 90 = 0

a = - 5

b = - 15

c = 90

x = \frac{​ - b \pm \sqrt ​ b ^{​ 2 ​ ​} - 4 a c ​ ​ ​ ​ ​}{​ 2 a ​}

x = \frac{​ - - 1 5 \pm \sqrt ​ ( - 1 5 ) ^{​ 2 ​ ​} - 4 \cdot - 5 \cdot 9 0 ​ ​ ​ ​ ​}{​ 2 \cdot - 5 ​}

x = \frac{​ - - 1 5 \pm \sqrt ​ ( - 1 5 ) ^{​ 2 ​ ​} - 4 \cdot - 5 \cdot 9 0 ​ ​ ​ ​ ​}{​ 2 \cdot - 5 ​}

Slide 45 - Slide

Drieterm oplossen

- 5 x^{​ 2 ​ ​} - 15 x + 90 = 0

a = - 5

b = - 15

c = 90

x = \frac{​ - b \pm \sqrt ​ b ^{​ 2 ​ ​} - 4 a c ​ ​ ​ ​ ​}{​ 2 a ​}

x = \frac{​ - - 1 5 \pm \sqrt ​ ( - 1 5 ) ^{​ 2 ​ ​} - 4 \cdot - 5 \cdot 9 0 ​ ​ ​ ​ ​}{​ 2 \cdot - 5 ​}

x = \frac{​ 1 5 \pm \sqrt ​ 2 2 5 - - 1 8 0 0 ​ ​ ​ ​ ​}{​ - 1 0 ​}

x = \frac{​ - - 1 5 \pm \sqrt ​ ( - 1 5 ) ^{​ 2 ​ ​} - 4 \cdot - 5 \cdot 9 0 ​ ​ ​ ​ ​}{​ 2 \cdot - 5 ​}

Slide 46 - Slide

Drieterm oplossen

- 5 x^{​ 2 ​ ​} - 15 x + 90 = 0

a = - 5

b = - 15

c = 90

x = \frac{​ - b \pm \sqrt ​ b ^{​ 2 ​ ​} - 4 a c ​ ​ ​ ​ ​}{​ 2 a ​}

x = \frac{​ - - 1 5 \pm \sqrt ​ ( - 1 5 ) ^{​ 2 ​ ​} - 4 \cdot - 5 \cdot 9 0 ​ ​ ​ ​ ​}{​ 2 \cdot - 5 ​}

x = \frac{​ 1 5 \pm \sqrt ​ 2 2 5 - - 1 8 0 0 ​ ​ ​ ​ ​}{​ - 1 0 ​}

x = \frac{​ 1 5 \pm \sqrt ​ 2 0 2 5 ​ ​ ​ ​ ​}{​ - 1 0 ​}

x = \frac{​ - - 1 5 \pm \sqrt ​ ( - 1 5 ) ^{​ 2 ​ ​} - 4 \cdot - 5 \cdot 9 0 ​ ​ ​ ​ ​}{​ 2 \cdot - 5 ​}

Slide 47 - Slide

Drieterm oplossen

- 5 x^{​ 2 ​ ​} - 15 x + 90 = 0

a = - 5

b = - 15

c = 90

x = \frac{​ - b \pm \sqrt ​ b ^{​ 2 ​ ​} - 4 a c ​ ​ ​ ​ ​}{​ 2 a ​}

x = \frac{​ - - 1 5 \pm \sqrt ​ ( - 1 5 ) ^{​ 2 ​ ​} - 4 \cdot - 5 \cdot 9 0 ​ ​ ​ ​ ​}{​ 2 \cdot - 5 ​}

x = \frac{​ 1 5 \pm \sqrt ​ 2 2 5 - - 1 8 0 0 ​ ​ ​ ​ ​}{​ - 1 0 ​}

x = \frac{​ 1 5 \pm \sqrt ​ 2 0 2 5 ​ ​ ​ ​ ​}{​ - 1 0 ​}

x = \frac{​ - - 1 5 \pm \sqrt ​ ( - 1 5 ) ^{​ 2 ​ ​} - 4 \cdot - 5 \cdot 9 0 ​ ​ ​ ​ ​}{​ 2 \cdot - 5 ​}

x = \frac{​ 1 5 \pm 4 5 ​ ​}{​ - 1 0 ​}

Slide 48 - Slide

Drieterm oplossen

- 5 x^{​ 2 ​ ​} - 15 x + 90 = 0

a = - 5

b = - 15

c = 90

x = \frac{​ - b \pm \sqrt ​ b ^{​ 2 ​ ​} - 4 a c ​ ​ ​ ​ ​}{​ 2 a ​}

x = \frac{​ - - 1 5 \pm \sqrt ​ ( - 1 5 ) ^{​ 2 ​ ​} - 4 \cdot - 5 \cdot 9 0 ​ ​ ​ ​ ​}{​ 2 \cdot - 5 ​}

x = \frac{​ 1 5 \pm \sqrt ​ 2 2 5 - - 1 8 0 0 ​ ​ ​ ​ ​}{​ - 1 0 ​}

x = \frac{​ 1 5 \pm \sqrt ​ 2 0 2 5 ​ ​ ​ ​ ​}{​ - 1 0 ​}

x = \frac{​ - - 1 5 \pm \sqrt ​ ( - 1 5 ) ^{​ 2 ​ ​} - 4 \cdot - 5 \cdot 9 0 ​ ​ ​ ​ ​}{​ 2 \cdot - 5 ​}

x = \frac{​ 1 5 \pm 4 5 ​ ​}{​ - 1 0 ​}

x = \frac{​ 1 5 + 4 5 ​ ​}{​ - 1 0 ​}

x = \frac{​ 1 5 - 4 5 ​ ​}{​ - 1 0 ​}

Slide 49 - Slide

Drieterm oplossen

- 5 x^{​ 2 ​ ​} - 15 x + 90 = 0

a = - 5

b = - 15

c = 90

x = \frac{​ - b \pm \sqrt ​ b ^{​ 2 ​ ​} - 4 a c ​ ​ ​ ​ ​}{​ 2 a ​}

x = \frac{​ - - 1 5 \pm \sqrt ​ ( - 1 5 ) ^{​ 2 ​ ​} - 4 \cdot - 5 \cdot 9 0 ​ ​ ​ ​ ​}{​ 2 \cdot - 5 ​}

x = \frac{​ 1 5 \pm \sqrt ​ 2 2 5 - - 1 8 0 0 ​ ​ ​ ​ ​}{​ - 1 0 ​}

x = \frac{​ 1 5 \pm \sqrt ​ 2 0 2 5 ​ ​ ​ ​ ​}{​ - 1 0 ​}

x = \frac{​ - - 1 5 \pm \sqrt ​ ( - 1 5 ) ^{​ 2 ​ ​} - 4 \cdot - 5 \cdot 9 0 ​ ​ ​ ​ ​}{​ 2 \cdot - 5 ​}

x = \frac{​ 1 5 \pm 4 5 ​ ​}{​ - 1 0 ​}

x = \frac{​ 1 5 + 4 5 ​ ​}{​ - 1 0 ​}

x = \frac{​ 1 5 - 4 5 ​ ​}{​ - 1 0 ​}

x = \frac{​ 6 0 ​ ​}{​ - 1 0 ​}

Slide 50 - Slide

Drieterm oplossen

- 5 x^{​ 2 ​ ​} - 15 x + 90 = 0

a = - 5

b = - 15

c = 90

x = \frac{​ - b \pm \sqrt ​ b ^{​ 2 ​ ​} - 4 a c ​ ​ ​ ​ ​}{​ 2 a ​}

x = \frac{​ - - 1 5 \pm \sqrt ​ ( - 1 5 ) ^{​ 2 ​ ​} - 4 \cdot - 5 \cdot 9 0 ​ ​ ​ ​ ​}{​ 2 \cdot - 5 ​}

x = \frac{​ 1 5 \pm \sqrt ​ 2 2 5 - - 1 8 0 0 ​ ​ ​ ​ ​}{​ - 1 0 ​}

x = \frac{​ 1 5 \pm \sqrt ​ 2 0 2 5 ​ ​ ​ ​ ​}{​ - 1 0 ​}

x = \frac{​ - - 1 5 \pm \sqrt ​ ( - 1 5 ) ^{​ 2 ​ ​} - 4 \cdot - 5 \cdot 9 0 ​ ​ ​ ​ ​}{​ 2 \cdot - 5 ​}

x = \frac{​ 1 5 \pm 4 5 ​ ​}{​ - 1 0 ​}

x = \frac{​ 1 5 + 4 5 ​ ​}{​ - 1 0 ​}

x = \frac{​ 1 5 - 4 5 ​ ​}{​ - 1 0 ​}

x = \frac{​ 6 0 ​ ​}{​ - 1 0 ​}

x = \frac{​ - 3 0 ​ ​}{​ - 1 0 ​}

Slide 51 - Slide

Drieterm oplossen

- 5 x^{​ 2 ​ ​} - 15 x + 90 = 0

a = - 5

b = - 15

c = 90

x = \frac{​ - b \pm \sqrt ​ b ^{​ 2 ​ ​} - 4 a c ​ ​ ​ ​ ​}{​ 2 a ​}

x = \frac{​ - - 1 5 \pm \sqrt ​ ( - 1 5 ) ^{​ 2 ​ ​} - 4 \cdot - 5 \cdot 9 0 ​ ​ ​ ​ ​}{​ 2 \cdot - 5 ​}

x = \frac{​ 1 5 \pm \sqrt ​ 2 2 5 - - 1 8 0 0 ​ ​ ​ ​ ​}{​ - 1 0 ​}

x = \frac{​ 1 5 \pm \sqrt ​ 2 0 2 5 ​ ​ ​ ​ ​}{​ - 1 0 ​}

x = \frac{​ - - 1 5 \pm \sqrt ​ ( - 1 5 ) ^{​ 2 ​ ​} - 4 \cdot - 5 \cdot 9 0 ​ ​ ​ ​ ​}{​ 2 \cdot - 5 ​}

x = \frac{​ 1 5 \pm 4 5 ​ ​}{​ - 1 0 ​}

x = \frac{​ 1 5 + 4 5 ​ ​}{​ - 1 0 ​}

x = \frac{​ 1 5 - 4 5 ​ ​}{​ - 1 0 ​}

x = \frac{​ 6 0 ​ ​}{​ - 1 0 ​}

x = \frac{​ - 3 0 ​ ​}{​ - 1 0 ​}

x = - 6

Slide 52 - Slide

Drieterm oplossen

- 5 x^{​ 2 ​ ​} - 15 x + 90 = 0

a = - 5

b = - 15

c = 90

x = \frac{​ - b \pm \sqrt ​ b ^{​ 2 ​ ​} - 4 a c ​ ​ ​ ​ ​}{​ 2 a ​}

x = \frac{​ - - 1 5 \pm \sqrt ​ ( - 1 5 ) ^{​ 2 ​ ​} - 4 \cdot - 5 \cdot 9 0 ​ ​ ​ ​ ​}{​ 2 \cdot - 5 ​}

x = \frac{​ 1 5 \pm \sqrt ​ 2 2 5 - - 1 8 0 0 ​ ​ ​ ​ ​}{​ - 1 0 ​}

x = \frac{​ 1 5 \pm \sqrt ​ 2 0 2 5 ​ ​ ​ ​ ​}{​ - 1 0 ​}

x = \frac{​ - - 1 5 \pm \sqrt ​ ( - 1 5 ) ^{​ 2 ​ ​} - 4 \cdot - 5 \cdot 9 0 ​ ​ ​ ​ ​}{​ 2 \cdot - 5 ​}

x = \frac{​ 1 5 \pm 4 5 ​ ​}{​ - 1 0 ​}

x = \frac{​ 1 5 + 4 5 ​ ​}{​ - 1 0 ​}

x = \frac{​ 1 5 - 4 5 ​ ​}{​ - 1 0 ​}

x = \frac{​ 6 0 ​ ​}{​ - 1 0 ​}

x = \frac{​ - 3 0 ​ ​}{​ - 1 0 ​}

x = - 6

x = 3

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Zelfstandig werken

Ga aan de slag met de opgaven van 8.6A
Overleg met je buurman/buurvrouw
Vragen? Steek je vinger op
Klaar? Begin aan 8.6B

timer

20:00

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ABC-formule

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