>Theory of Functions>How to Find Intersection Between Graphs in GeoGebra

How to Find Intersection Between Graphs in GeoGebra

You can either use CAS, or Algebra View and Graphics View together, to find the points of intersection between graphs. Instructions for both methods are detailed below.

GeoGebra Instruction 1

Using `CAS`

1.: Open CAS under View in Menu.
2.: Type $f (x)$ in CAS as

f(x) := $\dots$

and press Enter. Do the same with $g (x)$ .
3.: In an empty row in CAS, type
f = g
and click Solve in Toolbar. You should get a list of solutions.
4.: For each of the solutions x in the list from Step 3, type
(x,f(x))
in an empty row in CAS and press Enter. GeoGebra then displays the points of intersection.

Screenshot of GeoGebra showing the intersection of a parabola and a line

GeoGebra Instruction 2

Using `Algebra View` and `Graphics View`

1.: Open Algebra View and Graphics View under View in Menu.
2.: Type $f (x)$ into Algebra View and press Enter. Do the same with $g (x)$ . These now appear as functions in Algebra View and as graphs in Graphics View.
3.: In Toolbar, click Intersect (it is under the same menu as the Point tool).
4.: Click both graphs. The order does not matter.
5.: You will now find the points of intersection displayed in Algebra View.

Screenshot of GeoGebra showing the intersection of a parabola and a line

If you wish, you can additionally choose the axes to find the intersection between a graph and the axes.

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Using CAS

Using Algebra View and Graphics View

Using `CAS`

Using `Algebra View` and `Graphics View`