Open a new GeoGebra
worksheet. I have selected Options > Labeling > No
New Objects. Place 5 points randomly. We'll find the polynomial of degree 4 that best fits these points. At the bottom right corner of your screen is the Command List. Open it up to see what commands are available to you. Select FitPoly. Type the F1 key to see what form its argument takes. You should see FitPoly[<list of points>, <degree of polynomial>] Lists are sets of objects delimited by braces { }. Type FitPoly[ { A, B, C, D, E }, 4 ] Now move the points and see what happens. Type Integral[f(x), 2, 6] to see its effects. Click the (?) icon to the left of the Input Bar for more information. 

GeoGebra has some nice random
number generation features. Enter P = (RandomBetween[1, 7], RandomBetween[1, 4] ) This generates a point with xcoordinate between 1 and 7 (inclusive) and ycoordinate between 1 and 4 (inclusive). Typing CtrlR (View > Recompute All Objects) will regenerate the random numbers. 

Create a slider named a and allow it to take values
from 5 to 5. Define f(x) = x^3 + a x Move the slider so a = 2. Type R = Root[ f(x) ] and E = Extremum[ f(x) ] See how GeoGebra creates multiple points and names. See how these values change as the slider is moved. 

One of the most powerful
commands is Sequence. Make a slider called r with values from 0 to 5. Make a slider called n with values from 1 to 100, incrementing by 1. Enter the command Sequence[ (r cos( i 2π/n), r sin(i 2π/n)), i, 0, n1 ] To enter the π symbol, type Altp. Be careful with parentheses. This creates a sequence of points (the first argument in the command) as i goes from 0 to n1. Just for fun, rightclick slider r and check Animation On. Notice how a little Play/Pause button appears in the lower left corner of the Graphics View. 