4.5 Square root functions

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

Good morning!

Schedule: 

• Square root functions learning goals 
• Square root functions theory 
• Worksheet 
• Evaluate learning goals 
• Feedback 

Square root functions: learning goals 

At the end of this lesson I can:

• draw the graph of a square root function 
• calculate the y-coordinate of an square root function when the x-coordinate is given
• simplify square roots and square root functions 

Theory A: Functions with square roots 

Why do all of these graphs stop at the positive side of the y-axis?

Theory A: Functions with square roots 

If we look at

y=√​x​​​

x	-4	-1	0	4	5
y	not possible	not possible	0	2	2.2

Why not possible?

You can never take the square root of a negative number!!!

y=√​(−4)​​​

Theory A: Functions with square roots 

Theory A: Functions with square roots 

(Prior knowledge)

How to draw a graph from a function:

1. Make a table from the function 
2. Plot the points from your table in the coordinate system
3. Draw a smooth line through the plotted points

We draw graphs from square root functions with the same steps!

x	0	2	5	8	12.5
y	0

y=√​2x​​​

y=√​2⋅(0)​​​=√​0​​​=0

0

1

2

3

3.5

3.16

4

4.61

5

5.2

Theory A: Functions with square roots

x	0	2	5	8	12.5
y	0	2	3.16	4	5

y=√​2x​​​

y=√​2⋅(2)​​​=√​4​​​=2

y=√​2⋅(5)​​​=√​10​​​≈3.16

y=√​2⋅(8)​​​=√​16​​​=4

y=√​2⋅(12.5)​​​=√​25​​​=5

Theory A: Functions with squares

x	0	2	5	8	12.5
y	0	2	3.16	4	5

y=√​2x​​​

Now plot the points 

And draw a smooth curve through the points

Theory B: Simplifying square root functions

you can simplify square root functions by splitting the terms:

 

√​16x​​​=√​16​​​⋅√​x​​​=4√​x​​​

√​8x​​​=√​8​​​⋅√​x​​​≈2.83√​x​​​

3√​4x​​​=3⋅√​4​​​⋅√​x​​​=3⋅2⋅√​x​​​=6√​x​​​

√​9x​2​​​​​=√​9​​​⋅√​x​2​​​​​=3⋅x=3x

Simplify

y=5√​6x​​​

1. y=30√​x​​​
2. y=12.25√​x​​​
3. y=2.45√​x​​​
4. y=√​30x​​​

Simplify

y=3+2√​0.15x​​​

1. y=3+0.77√​x​​​
2. y=3+0.3√​x​​​
3. y=5+0.77√​x​​​
4. y=3+√​0.3x​​​

Take out your diaries! 

Homework: 

H2c              p.157-158: #61-68

                     Worksheet (google classroom): 

                     #1-5 (mijnschrift.nl)

This is homework for Monday 22-2-2021

Square root functions: learning goals 

At the end of this lesson I can:

• draw the graph of a square root function 
• calculate the x-coordinate when the y-coordinate is given
• calculate the y-coordinate when the x-coordinate is given
• simplify square roots and square root functions 

How many learning goals did you achieve today?

0

1

2

3

4