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Generating Equations jko

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.
1 / 28
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Slide 1: Diapositive
WiskundeMiddelbare schoolvwoLeerjaar 2

Cette leçon contient 28 diapositives, avec quiz interactifs et diapositives de texte.

Éléments de cette leçon

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.

Slide 1 - Diapositive

Page 128 
Ex. 68

Slide 2 - Diapositive

How to work this out?

x​2​​=x+6

Slide 3 - Diapositive

How to work this out?

x​2​​=x+6
x​2​​−x−6=0

Slide 4 - Diapositive

How to work this out?

x​2​​=x+6
x​2​​−x−6=0
Factorising:

Number 1
Number 2
Sum
Product

Slide 5 - Diapositive

How to work this out?

x​2​​=x+6
x​2​​−x−6=0
Factorising:

Number 1
Number 2
Sum   -1
Product

Slide 6 - Diapositive

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

Slide 7 - Diapositive

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

Slide 8 - Diapositive

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

Slide 9 - Diapositive

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

Slide 10 - Diapositive

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

Slide 11 - Diapositive

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

Slide 12 - Diapositive

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

Slide 13 - Diapositive

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

Slide 14 - Diapositive

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

Slide 15 - Diapositive

Page 128 
Ex. 68
x= -3 or x= 2

Slide 16 - Diapositive

Page 128 
Ex. 68
x= -3 or x= 2 
You can substitute x in both formula's

Slide 17 - Diapositive

Page 128 
Ex. 68
x= -3 or x= 2 
You can substitute x in both formula's

Slide 18 - Diapositive

What are the coordinates of the intersection points?

Slide 19 - Question ouverte

Page 131 ex. 75

Slide 20 - Diapositive

Page 131 ex. 75
Can we generate a formula?

Slide 21 - Diapositive

what is the Pythagorean theorem again?
A
a=b+c
B
a+b=c
C
a​2​​+b​2​​+c​2​​=0
D
a​2​​+b​2​​=c​2​​

Slide 22 - Quiz

You're allowed to use the Pythagorean theorem in :
A
an obtuse angle
B
a right angle
C
an reflex angle
D
an acute angle

Slide 23 - Quiz

Tekst
Obtuse angle
Right angle
Reflex angle
Acute angle

Slide 24 - Question de remorquage

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

Slide 25 - Diapositive

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

Slide 26 - Diapositive

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

Slide 27 - Question ouverte

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!

Slide 28 - Diapositive

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