Chapter 4: Squares and square roots prior knowledge

• Wiskunde
• Middelbare school
• havo, vwo
• Leerjaar 2

Good morning!

Schedule: 

• Chapter 4 learning goals 
• Prior knowledge learning goals
• Squares 
• Work on your homework 

Squares and
square roots

Chapter 4: squares and square roots

At the end of the chapter I can: 

- explain if the graph of a quadratic function is a smiley or a frowny parabola

- calculate with square roots 

- simplify square roots 

- work with square roots in functions 

- write square roots as powers 

- explain what rational and irrational numbers are 

Prior knowledge: squares 

At the end of this lesson I can: 

- calculate the square of any number

- name the order of operations including squares

-calculate y for quadratic functions 

- draw the graph of a quadratic function

We say: "The square of 8 is 64"

           =   "8 squared" 

                        or 

          "8 to the power of 2"

8​2​​=8⋅8=64

We can calculate          without a calculator!!

8​2​​

Theory A: basic calculations with squares 

110​2​​

We know: 

Now:                   12 100

And:                    1,21

11​2​​=121

110​2​​=

1.1​2​​=

When you square a number with one zero at the end,

The answer gets 2 zeros at the end.

When the komma is moved one place, 

The komma in the square is moved 2 places

Match the answers with the problems

7​2​​=

−7​2​​=

(−7)​2​​=

49

-49

49

20​2​​=

1. 4
2. 4000
3. 0,4
4. 400

0.6​2​​=

1. 36
2. 3,6
3. 0,36
4. 360

Theory B: Order of operations

1. 

2.

3. 

4.

Calculate inside the brackets 

Evaluate powers/squares

Multiply and divide from left to right

Add and substract from left to right

Theory C: Quadratic functions

In a function you can replace x by any number! 

                                     is a quadratic function. 

For x = 6, we get 

For x =    , we get 

y=−3x​2​​+4

y=−3⋅(6)​2​​+4=−3⋅36+4

=−108+4=−104

​4​​3​​

y=−3⋅(​4​​3​​)​2​​+4=−3⋅​16​​9​​+4

=−​16​​27​​+4=−​16​​27​​+​1​​4​​=−​16​​27​​+​16​​64​​

=37

Theory C: Quadratic functions

How to draw the graph of a quadratic function:

I want to draw the graph of 

1. Make a table

2. This gives us the points: (-2,2), (-1,-1), (0,-2), (1,-1), (2,2)

y=x​2​​−2

x	-2	-1	0	1	2
y	2	-1	-2	-1	2

Theory C: Quadratic functions

3. We draw the points in a coordinate plane.

4. We draw a smooth curve through the points.

x	-2	-1	0	1	2
y	2	-1	-2	-1	2

Consider the function
Calculate y for x = -5

y=2x​2​​+3

Take out your diaries!

Homework: 

h2f                  p. 136-137: #2a-f, 4, 5a-f, 6, 7, 8a

This is homework for Monday 25-1-2021

Prior knowledge: squares 

At the end of this lesson I can: 

- calculate the square of any number

- name the order of operations including squares

- calculate y for quadratic functions 

- draw the graph of a quadratic function

How many learning goals did you achieve today?

1

2

3

4