TTO1 Relations recap II

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• Middelbare school
• havo, vwo
• Leerjaar 1

Welcome to maths

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- Pen

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• Open your book on p. 59 and read the text
• Go to p. 62 and write down what you know in your notebook without reading the text on the page. 

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Today

• Recap C3 
• Do exercises
• Prepare for test 

Add a picture of this exercise:

• Draw a coordinate system. Use a scale from -10 to 10 for both axes. Use a step size of 2 for both axes. 
• Plot the following points: A(4,3), B(-7,3), C(9,-6)

Set up a formula for the following coordinates:
(0,4), (1,6), (2,8) and (3,10)

Which values do you need in the table?

x	-3	-2	-1	0	1
y	....	....	....	....	....

y=−2x​2​​+4

1. 40; 20; 8; 4 ; 8
2. -8; -4; 0; 4 ; 0
3. -14 ; -4 ; 2 ; 4 ; 2
4. ; -32 ; -12 ;0; 4 ; 0

§3.1 (skip quadrants)

• Draw a coordinate system 
• Plot points and give coordinates (ordered pair)
•  Origin, x-axis, y-axis, gridpoint, coordinates (ordered pair)

§3.2 Relationships

1. Express relationship not in words , but a formula
2. Three times as large as...., six smaller than..., three times larger..., squared, 10 minus the x-coordinate, equal to 1 and independant of,.......
3. Replace 'x' for a number to get 'y' for coordinates
4. Table of values 
5. Calculate the y-coordinate, set up a formula, read off coordinates, draw a graph

Ga de punten langs. Een krul wanneer ze het beheersen. Tel aantal krullen. Aantal krullen staat gelijk aan emoji. Dus 4 krullen, dan 4e emoji van links

§3.3 Formulas and graphs

1. Multiplication sign as a 'dot' or left out completely
2. Order of operations when calculating a y-coordinate
3. 1 and -1? Leave the 1 out when in front of a variable (letter)
4. Draw a graph by making a table of values,
   draw a coordinate system with a suitable scale,
   plot the points and connect them. 
5. Calculate the y-coordinate, set up a formula, read off coordinates, draw a graph

De leerlingen schrijven op wat de voorkennis is. Wat zijn ze dus al tegengekomen in §1 en §2.

§3.4 Linear and quadratic relations

1. Linear relationship --> graph is a line (constant rate), 
   number in front of 'x' is the amount of change per step
2. Quadratic relationship --> square, parabola (upward/downward),
   vertex
3. Brackets are possible in a formula 

y=−2x​2​​+4

y=−2x​​​+4

Positive number in front of x^2

Negative number in front of x^2

y=2x​2​​+4

Vraag de leerling welke formule lineair is

§3.5 Variables

1. Other relationships than the x- and y-coordinates
2. Variables--> Independent (x) and dependent (y)
3. Tables and graphs --> familiar?
4. 
   

y=−2x​2​​+4

Linear graph is a line. You need three points to draw this line

Quadratic graph (parabola) is a curve and you need at least seven points with the vertex in the middle

y=2x​​​+4

x	top	independent	horizontal
y	bottom	dependent	vertical

Copy the table

What is wrong with this parabola
for the formula

y=3+x​2​​

What is wrong with this graph for formula 

y = -2x + 1

What is wrong with the formula?

y=−(x−2)​2​​−5

x=3

y=−(3−2)​2​​−5

y=−(−1)​2​​−5

y=1−5

y=−4

Check your work

3-2 = 1 and not -1

y=−(1)​2​​−5=−1−5=−6

What is wrong with this calculation?
Write down the correct answer

y=5−4(x+1)​​​

x=​2​​1​​

y=5−4(​2​​1​​+1)

y=5−4⋅1​2​​1​​

y=1⋅1​2​​1​​

y=1​2​​1​​

Check your work

Order of operations. First multiplying and then adding or subtracting. 

y=5−6=−1

What is wrong with this calculation?
Write down the correct answer

What is wrong with this formula?

y=x+3

x	1	2	3	4	5
y	3	6	9	12	15

Good luck. You can do it!! 

Questions? You can reach me via Teams