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 and then use a slider investigate the effects of .

**Note: **This tutorial is updated for GeoGebra 4.2**. **

**Graphing Functions**

- Open GeoGebra and be sure the the
*Algebra and Graphics*view is selected for the*Perspective*menu. - To graph , type
*y*= 2*x*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. - Type the following equations: y = 3x, y = 4x , y = -8x, and press the ENTER key after each equation.
- Type more equations of the form where is any real number.
- How does the value of affect the appearance of the graph of the function ?

**Using Sliders**

To avoid typing over and over again for varying values , 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 , where and are real numbers.

**Instructions**

**Notes:**

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

ikaw ba nag program nyan guile?

it’s a freeware. i just created a graph. you can find the website ate http://www.geogebra.org

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