04-MP2

The following exercise will could be very useful to anyone who missed class when we discussed how the values of a, h & k affect the graph of y=**a**|x-**h**|+**k** when these values change.

You will need to go to the Grapher tool described in the video below. If you feel brave, you can just click the [|here] and go to it. However, the video below gives a little bit of description about the the graphing tool works. So, it might be useful.
 * Part One - Going to the Grapher Tool and Graping f(x)=a|x-h|+k**

Once you are there, please enter a|x-b|+c in the graphing window and hit the **Graph** button. Before you go any further, use the sliders to make sure that //a=1, h=0 and k=0//. Note that a is the same that we used in class with our notes. The Grapher tool does not allow us to use the letters h & k. So, just use b instead of the letter h and c instead of the letter k. __Just know that everytime we say b here we mean h and everytime we say k here we mean c.__

This video describes how to access a graphing tool that allows you to recreate the Sketchpad Demo that I did in class without the sketchpad document. It uses an internet based graphing tool that works in a similar fashion. Feel free to message and post discussion around using it. It might be neat to use it to check this assignment.



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The following questions will help you "play along" with the notes found on slide 6 of the notes from class for this lesson. Click [|here] to get them.
 * Part Two-Seeing How the Value of "h" Affects the Graph of y=|x|**

1. If you need to, move the sliders so that a=1, h=0 & k=0.

2. Pick a positive value for h. Move the slider so that h (in this case b) becomes that value? How did this "TRANSFORM" the graph?

3. Form a hypothesis about how the graph will change when you pick a negative value for h (in this case b). Move the slider so that h (in this case b) becomes that value? How did this "TRANSFORM" the graph?

4. What value would h have to be for the graph of y=|x| to slide horizontally -4 units?

The following questions will help you "play along" with the notes found on slide 6 of the notes from class for this lesson. Click [|here] to get them.
 * Part Three-Seeing How the Value of "k" Affects the Graph of y=|x|**

1. Move the sliders so that a=1, h=0 & k=0.

2. Pick a positive value for k. Move the slider so that k (in this case c) becomes that value? How did this "TRANSFORM" the graph?

3. Form a hypothesis about how the graph will change when you pick a negative value for k (in this case c). Move the slider so that k (in this case c) becomes that value? How did this "TRANSFORM" the graph?

4. What value would k have to be for the graph of y=|x| to slide vertically 2.5 units?

The following questions will help you "play along" with the notes found on slide 7 of the notes from class for this lesson. Click [|here] to get them.
 * Part Four-Seeing How the Value of "a" Affects the Graph of y=|x|**

1. Move the sliders so that a=1, h=0 & k=0.

2. Pick a a value for a such that a>1. Move the slider so that a becomes that value. How did this transform the graph?

3. Pick a positive value for a that is less than 1. (I.e. 0<a<1). Move the slider so that a becomes that value. How did this transform the graph?

4. Move the slider so at a=-1. How did this transform the graph?

5. Form a hypothesis about what will happen if a=-3. Move the slider so that a becomes equal to -3. Was your hypotheses correct?