Exploring Square Root Equations in VERTEX FORM in
Geometer’s Sketchpad
Name: _____________________________________
Start Up Directions:
1.) Graph | Define New Coordinate System
2.) Go to the Mac HD. Open the Applications Folder. Open the Sketchpad Folder.
Open the Samples Folder. Open the Sliders File. (This will add the sliders tool to
Sketchpad). Minimize the Sliders File.
3.) Click
at the bottom of the Toolbar. Select Sliders. Select Basic Horizontal
Sliders.
4.) In the GSP document. Click and move the mouse three times to create three
sliders. Hit the esc key at the top left of the Mac to exit this mode.
5.) Click
on the Toolbar.
• Click on the second “a= ____” at the top. Choose the Label Tab. Change the
label to h. Click on the “a” that corresponds to the second slider. Change the
label to h.
• Click on the third “a= ____” at the top. Choose the Label Tab. Change the
label to k. Click on the “a” that corresponds to the third slider. Change the
label to k.
6.) Click on the Green Point on the Slider to move it and change the values of a,h,
and k to 1.
7.) Graph | Plot new Function. Click the parameters in the sketch to enter them
(a=, h = , k = ). Enter a*sqrt(x-h)+k.
Select the green dot on the slider that corresponds with parameter a.
Describe the two things that happen to the graph as you change parameter a.
1.)________________________________________________________________
2.) _________________________________________________________________
What special property does the graph have when a = 0 ? _________________________
Select the green dot on the slider that corresponds with parameter h.
What happens to the graph as you change the parameter h? ______________________
_____________________________________________________________________
What special property does the graph have when h = 0? ______________________
_____________________________________________________________________
Exploring Square Root Equations in VERTEX FORM in
Geometer’s Sketchpad
Select the green dot on the slider that corresponds with parameter k.
What happens to the graph as you change the parameter k? ______________________
_____________________________________________________________________
What special property does the graph have when k = 0 ? ______________________
_____________________________________________________________________
Adjust the sliders to that a = 1, h = 0 and k = 0.
Write the equation of the graph. ____________________________
(This is the parent function for the family of vertex form quadratic functions)
Plot the parent function on the graph in red.
Adjust the sliders so that a = 1, h = 3, and k = -4.
Where is the vertex of the new graph? _____________________________
Write the new equation of the graph ______________________________
Describe the translation of the parent function to attain the new graph_____________
_______________________________________________________
Adjust the sliders so that a = 5, h = 3, and k = -4.
Where is the vertex of the new graph? _____________________________
Write the equation of the new graph ______________________________
Describe the translation of the parent function to attain the new graph_____________
_______________________________________________________
Adjust the sliders so that a = -5, h = 3, and k = -4.
Where is the vertex of the new graph? _____________________________
Write the equation of the new graph ______________________________
Describe the translation of the parent function to attain the new graph_____________
_______________________________________________________
Adjust the sliders so that a = 3, h = -5, and k = 2.
Where is the vertex of the new graph? _____________________________
Write the equation of the new graph ______________________________
Describe the translation of the parent function to attain the new graph_____________
_______________________________________________________
Exploring Square Root Equations in VERTEX FORM in
Geometer’s Sketchpad
Adjust the sliders so that a =
1
, h = -2, and k = -5.
4
Where is the vertex of the new graph? _____________________________
Write the equation of the new graph ______________________________
Describe the translation of the parent function to attain the new graph_____________
_______________________________________________________
Adjust the sliders so that a =
1
− , h = -1, and k = 4.
2
Where is the vertex of the new graph? _____________________________
Write the equation of the new graph ______________________________
Describe the translation of the parent function to attain the new graph_____________
_______________________________________________________