Lineaire en kwadratische vergelijkingen

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Slide 1: Diapositive

WiskundeMiddelbare schoolhavoLeerjaar 3

Cette leçon contient 30 diapositives, avec quiz interactifs et diapositives de texte.

Éléments de cette leçon

Slide 1 - Diapositive

A D^{​ 2 ​ ​} + A B^{​ 2 ​ ​} = B D^{​ 2 ​ ​}

4.2^{​ 2 ​ ​} + 12^{​ 2 ​ ​} = B D^{​ 2 ​ ​}

B D = \sqrt ​ 161.64 ​ ​ ​

B D \approx 12.71

Slide 2 - Diapositive

A D^{​ 2 ​ ​} + A B^{​ 2 ​ ​} = B D^{​ 2 ​ ​}

4.2^{​ 2 ​ ​} + 12^{​ 2 ​ ​} = B D^{​ 2 ​ ​}

B D = \sqrt ​ 161.64 ​ ​ ​

B D \approx 12.71

M F = \frac{​ 1 2 . 7 1 2 ​ ​}{​ 2 ​} \approx 6.36

Slide 3 - Diapositive

A D^{​ 2 ​ ​} + A B^{​ 2 ​ ​} = B D^{​ 2 ​ ​}

4.2^{​ 2 ​ ​} + 12^{​ 2 ​ ​} = B D^{​ 2 ​ ​}

B D = \sqrt ​ 161.64 ​ ​ ​

B D \approx 12.71

M F = \frac{​ 1 2 . 7 1 2 ​ ​}{​ 2 ​} \approx 6.36

cos (∠ F) = \frac{​ 6 . 3 6 ​ ​}{​ 7 . 1 ​}

Slide 4 - Diapositive

A D^{​ 2 ​ ​} + A B^{​ 2 ​ ​} = B D^{​ 2 ​ ​}

4.2^{​ 2 ​ ​} + 12^{​ 2 ​ ​} = B D^{​ 2 ​ ​}

B D = \sqrt ​ 161.64 ​ ​ ​

B D \approx 12.71

M F = \frac{​ 1 2 . 7 1 2 ​ ​}{​ 2 ​} \approx 6.36

∠ F = cos^{​ - 1 ​ ​} (\frac{​ 6 . 3 6 ​ ​}{​ 7 . 1 ​})

cos (∠ F) = \frac{​ 6 . 3 6 ​ ​}{​ 7 . 1 ​}

Slide 5 - Diapositive

A D^{​ 2 ​ ​} + A B^{​ 2 ​ ​} = B D^{​ 2 ​ ​}

4.2^{​ 2 ​ ​} + 12^{​ 2 ​ ​} = B D^{​ 2 ​ ​}

B D = \sqrt ​ 161.64 ​ ​ ​

B D \approx 12.71

M F = \frac{​ 1 2 . 7 1 2 ​ ​}{​ 2 ​} \approx 6.36

∠ F = cos^{​ - 1 ​ ​} (\frac{​ 6 . 3 6 ​ ​}{​ 7 . 1 ​})

cos (∠ F) = \frac{​ 6 . 3 6 ​ ​}{​ 7 . 1 ​}

∠ F \approx 26.4

Slide 6 - Diapositive

M T = 9.1 - 6 = 3.1

Slide 7 - Diapositive

sin (∠ F) = \frac{​ 3 . 1 ​ ​}{​ 7 . 1 ​}

M T = 9.1 - 6 = 3.1

Slide 8 - Diapositive

∠ F = sin^{​ - 1 ​ ​} (\frac{​ 3 . 1 ​ ​}{​ 7 . 1 ​})

sin (∠ F) = \frac{​ 3 . 1 ​ ​}{​ 7 . 1 ​}

M T = 9.1 - 6 = 3.1

Slide 9 - Diapositive

∠ F = sin^{​ - 1 ​ ​} (\frac{​ 3 . 1 ​ ​}{​ 7 . 1 ​})

sin (∠ F) = \frac{​ 3 . 1 ​ ​}{​ 7 . 1 ​}

∠ F \approx 25.9 °

M T = 9.1 - 6 = 3.1

Slide 10 - Diapositive

y = - 2 x^{​ 2 ​ ​} + 8 x + 10

Slide 11 - Diapositive

y = - 2 x^{​ 2 ​ ​} + 8 x + 10

a = - 2

b = 8

c = 10

Slide 12 - Diapositive

y = - 2 x^{​ 2 ​ ​} + 8 x + 10

a = - 2

b = 8

c = 10

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

Slide 13 - Diapositive

y = - 2 x^{​ 2 ​ ​} + 8 x + 10

a = - 2

b = 8

c = 10

x = \frac{​ - 8 + - \sqrt ​ 8 ^{​ 2 ​ ​} - 4 \cdot - 2 \cdot 1 0 ​ ​ ​ ​ ​}{​ 2 \cdot - 2 ​}

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

Slide 14 - Diapositive

y = - 2 x^{​ 2 ​ ​} + 8 x + 10

a = - 2

b = 8

c = 10

x = \frac{​ - 8 + - \sqrt ​ 8 ^{​ 2 ​ ​} - 4 \cdot - 2 \cdot 1 0 ​ ​ ​ ​ ​}{​ 2 \cdot - 2 ​}

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

x = \frac{​ - 8 - 1 2 ​ ​}{​ - 4 ​}

x = \frac{​ - 8 + 1 2 ​ ​}{​ - 4 ​}

Slide 15 - Diapositive

y = - 2 x^{​ 2 ​ ​} + 8 x + 10

a = - 2

b = 8

c = 10

x = \frac{​ - 8 + - \sqrt ​ 8 ^{​ 2 ​ ​} - 4 \cdot - 2 \cdot 1 0 ​ ​ ​ ​ ​}{​ 2 \cdot - 2 ​}

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

x = \frac{​ - 8 - 1 2 ​ ​}{​ - 4 ​}

x = \frac{​ - 8 + 1 2 ​ ​}{​ - 4 ​}

x = 5

x = - 1

Slide 16 - Diapositive

Slide 17 - Diapositive

g = 1 + \frac{​ 3 ​ ​}{​ 1 0 0 ​} = 1.03

y = b \cdot g^{​ x ​ ​}

Slide 18 - Diapositive

y = b \cdot g^{​ x ​ ​}

y = 4.8 \cdot 1.03^{​ 3 ​ ​}

Slide 19 - Diapositive

, dus 5,25 miljoen kijkers

y = b \cdot g^{​ x ​ ​}

y = 4.8 \cdot 1.03^{​ 3 ​ ​}

y \approx 5.25

Slide 20 - Diapositive

Lineaire en kwadratische vergelijkingen

Pak je Ipad, schrift en rekenmachine

Slide 21 - Diapositive

Los op:

3 x + 2 = 5 x - 8

timer

0:45

Slide 22 - Diapositive

x = ...

Slide 23 - Question ouverte

Los op:

3 x + 2 = 5 x - 8

Slide 24 - Diapositive

Los op:

3 + 5 (3 x - 1) = 7 x + 10

Slide 25 - Diapositive

Los op:

3 x^{​ 2 ​ ​} - 9 x - 30 = 0

timer

2:00

Slide 26 - Diapositive

x = ... of x = ...

Slide 27 - Question ouverte

Los op:

3 x^{​ 2 ​ ​} - 9 x - 30 = 0

Slide 28 - Diapositive

Vind de snijpunten van de twee parabolen

y = 4 x^{​ 2 ​ ​} - 5 x + 17

y = 3 x^{​ 2 ​ ​} + 5 x - 8

Slide 29 - Diapositive

Zelf aan de slag

Ga aan de slag met de slag met de opgaven van 13.1.
Overleg met je buurman/buurvrouw
Vragen of klaar? Steek je vinger op.

Slide 30 - Diapositive

Lineaire en kwadratische vergelijkingen

Éléments de cette leçon

Slide 1 - Diapositive

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Slide 3 - Diapositive

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Slide 9 - Diapositive

Slide 10 - Diapositive

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Slide 13 - Diapositive

Slide 14 - Diapositive

Slide 15 - Diapositive

Slide 16 - Diapositive

Slide 17 - Diapositive

Slide 18 - Diapositive

Slide 19 - Diapositive

Slide 20 - Diapositive

Slide 21 - Diapositive

Slide 22 - Diapositive

Slide 23 - Question ouverte

Slide 24 - Diapositive

Slide 25 - Diapositive

Slide 26 - Diapositive

Slide 27 - Question ouverte

Slide 28 - Diapositive

Slide 29 - Diapositive

Slide 30 - Diapositive

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