Download Geogebra quick start

Open a blank page
Equations With Degree 1 or 2
(a)
Equations of degree 1 or 2 can be
entered either implicitly or as y =
(b)
For ease of use these equations should
be given a name (a lower case letter)
Eg: Entering a:2x+3y = 6 gives a
straight line with name a
The “Command” Menu



This gives 69 different commands that can be
applied to the diagram.
Format
(a) Select a command
(b) For simple commands enter the name of the
object in the square brackets.
Eg: To find the slope of the line, choose “slope”
from the menu and type ‘a’ in the brackets
Drawing a perpendicular to a
line from a point




Choose point from the point menu
(second from left)
Click anywhere on the screen
Choose perpendicular line (fourth menu
from the left)
Click on the point and then on the line
Using The Object List



Right clicking on any object in the object list or
on the diagram gives a choice that includes
(a) deleting the object
(b) editing the object
(c) changing the format of an equation
Eg: Right clicking on the equation of a straight
line gives a choice of
ax+by = c; y = mx +c or parametric form
Using the mouse to point to any object on the
list or on the diagram tells you what it is.
Using Sliders

Sliders allow you to enter a pro-numeral as
part of an equation and observe what
happens as the pro-numeral changes

Eg: Sliders can be used to observe what
happens as values of m and c change
when the equation y = m x + c is entered
Investigating
y = mx +c







The slider icon is in the measure menu (6th icon from
the left)
Highlight this icon, then click anywhere to deposit
the slider.
Change setting if needed, then select “Apply”
Repeat this process to create a second slider.
Right click on the first slider, choose “rename” and
change to m.
Rename the second slider c
Enter a:y = m*x +c Use your sliders to change
the values of m and c
Investigating Circles




Create three sliders and rename them
h, k and r.
Enter c: (x-h)^2+(y-k)^2=r^2
Observe what happens as h, k and r
change
Use commands to find the centre and the
radius of your circle
The Circle
More Complex Functions


These must be entered using function notation
A function entered as “f(x) =“ has the name f.
For any polynomials GeoGebra can
(a) Find turning points (extremum) and
inflexion points
(b) Find roots
(c) Draw first and second derivatives
Cubics




With the help of three sliders enter
f(x) = (x-a)(x-b)(x-c)
Investigate the effect of changing a, b
and c
Using commands add the roots,
extremum and inflexion point to your
diagram.
Draw the first and second derivatives:
derivative[f] and derivative[f,2]
Trigonometric Functions






Function notation must be used
The argument of the trig function must
be in brackets
Right click on the x axis and choose –
properties – units and select π
Enter f(x) = a*sin(b*(x-h)) + k and play
The root in the interval [1, 2] can be
found with root[f, 1, 2]
Derivatives can be found
A Trigonometric Example
Lower and Upper Sums





Enter a slider with a range of values from 5
to 100, label it n
Enter your function. Eg f(x) = 0.5x^2 + 2
To find a lower sum from 0 to 4 with n
rectangles enter lowersum[f,0,4,n]
Enter Uppersum[f,0,4,n]
Play with the slider.
Integration Example
The angle in a semicircle







Right click on the axes and turn them off
Draw a circle (Circle menu)
Draw a line through the centre and any point on the
circle (Circle menu)
Find the intersection points of the line and the circle
(command menu)
Draw a triangle through the points of intersection
and any other point on the circle (line menu)
Choose angle from the measure menu and click on
any angle of the polygon
Use the arrow (top left icon) to change the diagram