Generating Equations jko

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 2

Goodmorning! Please enter this lesson by using the code in the left-hand corner.

Aim of this lesson:

• Learn how to find the intersection points of a linear and a quadratic equation
• Learn how to generate a formula.

The product of two consecutive even numbers is 288.

Which two numbers?

(try to solve this by making an equation) Remember your answer, don't put this in a chat.

Page 128 

Ex. 68

How to work this out?

x​2​​=x+6

How to work this out?

x​2​​=x+6

x​2​​−x−6=0

How to work this out?

x​2​​=x+6

x​2​​−x−6=0

Factorising:

Number 1

Number 2

Sum

Product

How to work this out?

x​2​​=x+6

x​2​​−x−6=0

Factorising:

Number 1

Number 2

Sum   -1

Product

How to work this out?

x​2​​=x+6

x​2​​−x−6=0

Factorising:

Number 1	Number 2	Sum -1	Product -6
-1	6	5	-6

How to work this out?

x​2​​=x+6

x​2​​−x−6=0

Factorising:

Number 1	Number 2	Sum -1	Product -6
-1	6	5	-6

How to work this out?

x​2​​=x+6

x​2​​−x−6=0

Factorising:

Number 1	Number 2	Sum -1	Product -6
-1	6	5	-6
-6	1	-5	-6

How to work this out?

x​2​​=x+6

x​2​​−x−6=0

Factorising:

Number 1	Number 2	Sum -1	Product -6
-1	6	5	-6
-6	1	-5	-6
-2	3	1	-6

How to work this out?

x​2​​=x+6

x​2​​−x−6=0

Factorising:

Number 1	Number 2	Sum -1	Product -6
-1	6	5	-6
-6	1	-5	-6
-2	3	1	-6
-3	2	-1	-6

How to work this out?

x​2​​=x+6

x​2​​−x−6=0

Factorising:

Number 1	Number 2	Sum -1	Product -6
-1	6	5	-6
-6	1	-5	-6
-2	3	1	-6
-3	2	-1	-6

How to work this out?

x​2​​=x+6

x​2​​−x−6=0

Factorising:

Number 1	Number 2	Sum -1	Product -6
-1	6	5	-6
-6	1	-5	-6
-2	3	1	-6
-3	2	-1	-6

(x−3)(x+2)=0

How to work this out?

x​2​​=x+6

x​2​​−x−6=0

Factorising:

Number 1	Number 2	Sum -1	Product -6
-1	6	5	-6
-6	1	-5	-6
-2	3	1	-6
-3	2	-1	-6

(x−3)(x+2)=0

x−3=0

x+2=0

or

How to work this out?

x​2​​=x+6

x​2​​−x−6=0

Factorising:

Number 1	Number 2	Sum -1	Product -6
-1	6	5	-6
-6	1	-5	-6
-2	3	1	-6
-3	2	-1	-6

(x−3)(x+2)=0

x−3=0

x+2=0

or

x=3 or x= -2

Page 128 

Ex. 68

x= -3 or x= 2

Page 128 

Ex. 68

x= -3 or x= 2 

You can substitute x in both formula's

Page 128 

Ex. 68

x= -3 or x= 2 

You can substitute x in both formula's

What are the coordinates of the intersection points?

Page 131 ex. 75

Page 131 ex. 75

Can we generate a formula?

what is the Pythagorean theorem again?

1. a=b+c
2. a+b=c
3. a​2​​+b​2​​+c​2​​=0
4. a​2​​+b​2​​=c​2​​

You're allowed to use the Pythagorean theorem in :

1. an obtuse angle
2. a right angle
3. an reflex angle
4. an acute angle

Tekst

Obtuse angle

Right angle

Reflex angle

Acute angle

Page 131 ex. 75

x

• Via Mario = 14 km
  
• So the distance From Mario -> Thomas = 14-x
• x2 + (14-x)2 = 102
• x2+196-28x+x2=100
• 2x2 -28x +96=0

Via Mario = 14 km
So the distance From Mario -> Thomas = 14-x
x2 + (14-x)2 = 102
x2+196-28x+x2=100
2x2 -28x +96=0

• Factorise! But first divide by 2.
  
• x2 -14x+48=0
  
• (x-6)(x-8)=0
  
• x-6 = 0 or x-8 = 0
  
• x=6 or x= 8
  

Back to the question of the first slide:
The product of two consecutive even numbers is 288. Which two numbers?

The product of two consecutive even numbers is 288.

Which two number?

(try to solve this by making an equation) Rember your answer don't put this in a chat

Aim of this lesson:

• Learn how to find the intersection points of a linear and a quadratic equation
• Learn how to generate a formula.

Homework: All combined exercises. Hand them in in Teams before next tuesday. There is an assignment in Teams!