Linear and quadratic solutions

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Slide 1: Slide

WiskundeMiddelbare schoolhavoLeerjaar 3

This lesson contains 29 slides, with interactive quizzes and text slides.

Items in this lesson

Linear and quadratic solutions

You need your Ipad, notebook and a calculator

Slide 1 - Slide

Today

Start (5 min)
'New' subject (15 min)
Bettermarks (15 min)
Second part explanation (15 min)
Bettermarks (25 min)
End lesson (5 min)

Slide 2 - Slide

Solve for x:

4 x + 2 = 6 x - 8

Slide 3 - Slide

Solve for x:

4 x + 4 = - 2 x + 34

timer

1:30

Slide 4 - Open question

4 x + 4 = - 2 x + 34

Slide 5 - Slide

13.1: Linear and quadratic solutions

To solve linear equations we use the balance method.

Example, solve:

Step 1: rearrange x terms

Step 2: rearrange constant terms

Step 3: divide

3 x + 8 = x - 13

2 x + 8 = - 13

2 x = - 21

x = - 10.5

Slide 6 - Slide

13.1: Linear and quadratic solutions

7 (2 x - 4) = 19 x + 9

Slide 7 - Slide

Remove the brackets

8 (6 x - 1)

timer

1:00

Slide 8 - Open question

Slide 9 - Slide

Bettermarks

15 minutes
Bettermarks 13.1 (up to exersize 9 should be doable)
Raise your finger if you have any questions or when you're finished
Communicate in English please

timer

15:00

Slide 10 - Slide

Quadratic solutions

Go to LessonUp again

You need your notebook

Slide 11 - Slide

Quadratic solutions

y = 2 x^{​ 2 ​ ​} + x - 7

Slide 12 - Slide

Find a, b and c in the formula

y = 2 x^{​ 2 ​ ​} + x - 7

Slide 13 - Open question

Find a, b and c in the formula

y = 2 x^{​ 2 ​ ​} + x - 7

Slide 14 - Slide

Quadratic solutions

y = 2 x^{​ 2 ​ ​} + x - 7

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

Slide 15 - Slide

Quadratic formula

3 x^{​ 2 ​ ​} + 18 x + 15 = 0

Slide 16 - Slide

Quadratic formula

3 x^{​ 2 ​ ​} + 18 x + 15 = 0

a = 3

b = 18

c = 15

Slide 17 - Slide

Quadratic formula

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 18 - Slide

Quadratic formula

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 19 - Slide

Quadratic formula

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 4 4 ​ ​ ​ ​ ​}{​ 6 ​}

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

Slide 20 - Slide

Quadratic formula

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 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 21 - Slide

Quadratic formula

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 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 22 - Slide

Quadratic formula

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 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 23 - Slide

Note: 13.3 Example Quadratic formula

Solve for x:

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 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 24 - Slide

Quadratic formula

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 = - 1

x = - 5

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

Slide 25 - Slide

Quadratic formula

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 = - 1

x = - 5

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

Slide 26 - Slide

Question 10 in Bettermarks

Slide 27 - Slide

Bettermarks

Bettermarks 13.1
Until the end of the lesson
Raise your finger if you have any questions or when you're finished
Communicate in English please

Slide 28 - Slide

Question 17

Slide 29 - Slide

Linear and quadratic solutions

Items in this lesson

Slide 1 - Slide

Slide 2 - Slide

Slide 3 - Slide

Slide 4 - Open question

Slide 5 - Slide

Slide 6 - Slide

Slide 7 - Slide

Slide 8 - Open question

Slide 9 - Slide

Slide 10 - Slide

Slide 11 - Slide

Slide 12 - Slide

Slide 13 - Open question

Slide 14 - Slide

Slide 15 - Slide

Slide 16 - Slide

Slide 17 - Slide

Slide 18 - Slide

Slide 19 - Slide

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