# GeoGebra Tutorial 4 – Graphs and Sliders

This is the fourth tutorial in the GeoGebra Intermediate Tutorial Series. If this is your first time to use GeoGebra, please read the GeoGebra Essentials Series first.

In this tutorial, we  use GeoGebra to investigate the effects of parameters of the equations of functions to the appearance of their graphs.  First, we type equations $y = mx$ and then use a slider investigate the effects of $m$.

Figure 1 – Sample Graphs created with GeoGebra

Note: This tutorial is updated for GeoGebra 4.2

Graphing Functions

1. Open GeoGebra and be sure the the Algebra and Graphics view is selected for the Perspective menu.
2. To graph $y = 2x$, type y = 2x in the input field. (The input field is the text box with the label Input located at the bottom of your GeoGebra window.) Press the ENTER key on your keyboard.
3. Type the following equations: y = 3x, y = 4x , y = -8x, and press the ENTER key after each equation.
4. Type more equations of the form $y = mx$ where $m$ is any real number.
5. How does the value of $m$affect the appearance of the graph of the function $y = mx$?

Using Sliders

To avoid typing over and over again for varying values $m$, we use the slider tool.  A slider is a visual representation of a number. This time, we add the parameter b. This means that we will explore the graph of the function of $y = mx + b$, where $m$ and$b$ are real numbers.

Instructions

 1.) Open the GeoGebra and be sure that Algebra and Graphics view is selected from the Perspective menu. 2.) Select the Slider tool and click on the Graphics view to display the Slider dialog box. 3.) In the Slider dialog box, change the slider’s name to m, change the interval to $-10$ to $10$ as shown below.Leave the other values as is and click the Apply button to finish. 4.) Adjust the position of your slider if necessary. Move the small black circle on your slider. What do you observe? 5.) To graph the function $y = mx$,  type y = mx in the Input box. 6.) Now, Move the small circle on your slider. What do you observe? 7.) Now, create a new Slider and name it $b$. Set the interval to $-10$ and $10$ and leave the other values as is. 8.) To change the function to $y = mx + b$, double click the graph to display the Redefine window, and then type y = mx + b. 9.) Now, move your $b$ slider. What do you observe? 10. ) How does the value of $b$ affect the appearance of the graph of the function $y = mx + b$? 11.)  As an exercise, graph the function $y = ax^2 + b$. Explain the effects of the parameters $a$ and $b$ to the graph of the function.

Notes:

1. The ^ symbol is used for exponentiation. Hence, we write $ax^2 + c$ as a*x^2 + c.
2. Instead of using $y$ in writing equations of functions, you can also use $f(x)$ for the function $f$.

## 17 thoughts on “GeoGebra Tutorial 4 – Graphs and Sliders”

1. I graphed a parabola y=(x-a)^2 + b using sliders for a and b. As you increase a (in the positive direction), the parabola SHOULD move left, according to the rules for horizontal transformations, but on GeoGebra, it moves the opposite direction. Any ideas? Have you found that this happens often?

• hmmm… shouldn’t it move to the right? Isn’t (a,b) the vertex of your parabola? if you move to (a+1,b), shouldn’t the parabola go to the right? :-)Try graphing the following manually: (x – 3)^2 + 1 and (x – 2)^2 + 1. I think the first one is at the right of the latter. (I might be wrong though).

• nevermind – figured out what my student was talking about – wasn’t taking into account the fact that the negative is already in the function.. duh. thanks for humoring me