3Tvwo §9.1 Square root functions

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 3

§9.1 Square root functions, skipping 2.

Now in more  normal measurements!  Notice that:

+ the graph seems vertical at the beginning; it almost is.

+ the starting point we call the 'boundary point'. Here: (0,0)

+ Question: Why are there no points with negative x values?

 + Answer: Fill in, in the next slide!

Why no points for x is negative?

Answer:

The formula is  f(x) = 

The root of a negative number is impossible.

That's why!

Exercise 2 you may skip, because we discussed this now!

√​x​​​

How to find the boundary point, when you have a formula, not a graph?

In the boundary point the x-value is 0,

because the root of a negative x-value is impossible.

So, to find the boundary point, we make the number under the root sign zero!

Other roots than           in a formula appear too:

For instance:

√​x​​​

Follow step by step, how we now can find the 

boundary point!

As is already said,  the expression under the root sign we make 0! !

√​x​​​

−4+√​2x​​​+10

You've doing fine ..........

+ following the Method to find the boundary point

+ now you may try to find it yourself!

+ what is a noob?

Now find the boundary point by yourself,

step by step!

STEP 1: Make the expression under the square root sign 0.

So you get:   '  ........................ = 0'

Key in, in next slide! Remember what to key in!

Step 1: .............

answer step 1:

6x + 42 = 0

STEP 2: Calculate the x coordinate of the 

boundary point. Key in, in next slide again.

Answer step 1 was:

6x + 42 = 0

A. 7          B.  -42

C. 5          D. -7

What is the x value?

1. 7
2. -42
3. 5
4. -7

Answer step 2:

Card Method:                                      

6x + 42 = 0

6x = -42

x = -7

step 3: 

Calculate the y coordinate of the 

boundary point. This is what you need:

x = -7, to be filled in, in:                           A. 42     B. -5

                                                                               C. 5           D. -7

1. 42
2. -5
3. 5
4. -7

Step 4, (rounding off the task):

boundary point is:

( -7, 5)

If you were not succesful in the previous slides, it's no Tragedy...

What counts more, is your trial and error. Because you learnt from it!

Finally....

     a few practical remarks:

+ skip exercise 2 (as I said already)

+ exercise 3b and 3d:  In order to make the 2 graphs, make a Double Table,          using the x values -1 to 9

+ exercise 7:  also include a slide of the Workbook drawing, please.

Homework time.

You may leave this Google Hangouts,

I will, too.

Enjoy your day!