Mr. Stephen Lange » Desmos/Geogebra Projects and Lessons

Desmos/Geogebra Projects and Lessons

All students should create an account at You can't save a graph without an account.  If they have a gmail account, they can log in with their G-mail account and password.

Log in before you get to work.

SAVE your graphs OFTEN.

Precalculus Desmos Art Project
Desmos Art Project

Desmos Explorations
Desmos Explorations

Algebra 1

Linear Equations
Making an A Project

Graph a Box
Make a Three Dimensional Looking Box Using lines with restricted domains.
1. Start with making a 4 point rectangle..... then make another one offset up and to the right.
Connect the corners to give the art depth. You may need to find the equation of a line given two points to make the connection.


Algebra 2

Conic Sections
Mr. Corneius's Lesson on Graphing Faces

McDonald's Arches


Linear Functions Project
 Write the equation of a line passing through the points ( 2 , 8 ) and (6 ,  2 )

Linear Model Project

The following table lists values of x and y.

Pupil A B C D E F G H I J
Math Score 45 83 65 62 71 52 69 72 58 64
Science Score 39 80 59 60 65 54 65 67 56 64

1. Plot the points on desmos (see Scatterplot/Linear Regression example).
2. Use a calculator or online tool to find the line of best fit using least squares regression
3. Put the line of best fit on your graph
4. Use text boxes in desmos to describe
   a. The meaning of the slope
   b. The meaning of the y-intercept

Quadratic Functions Project

St Louis Arch-
McDonald's Arches
A Full McDonald's Meal

Quadratic Forms
1. Graph a parabola written in vertex form whose vertex is (-5,2) that passes through (-4,5)
2. Graph a parabola written in standard form whose vertex is (4,4) that passes through (0,0) [hint- it opens down]
3. Graph a parabola in factored form whose x intercepts are 4 and -2.

Find a Quadratic Given Three Points
Curve Fitting Project 1
Graph the points (-2,16) (0 , 2 ) and ( 3, 4)
then use y=ax^2+bx+c to create a three by three system of equations. Solve for a, b, and c
Check your work on the applet: Applet

Polynomial Function Projects
1. Graph a polynomial that has roots of -3, 0 and 2--. Write it in full polynomial form and show that it is the same graph.
2. Graph a polynomial that has the following roots and multiplicities
   Root: -3 Multiplicity 2
  Root -1  Multiplicity 1
  Root 2  Multiplicity 3
  Root 4 Multiplicity 1

Rational Function Projects
Rational Example of holes and poles

1. Graph a rational expression that has vertical asymptotes at x=2 and x=-1 and a horizontal asymptote at y= 3

Exponential Projects

Exponential Growth: Compounding Interest
I invest $10,000 into a savings bond that provides 4% interest compounded monthly.
Model the story in Desmos. Change the window of your graph so I can see how much money you will make over 30 years. Show how much $ I will have in 10 years and how long it will take to double

Exponential Decay: Bouncy Ball
A bouncy ball is dropped from a height of 27 inches... It bounces up 2/3 of its original height after each bounce
Draw a graph to model the height of the ball at each bounce

Logarithmic Projects:

Trig Functions
Biorhythms Desmos
Sunrise, Sunset


Scatterplot and Linear Regression

Transformation of Points


Limits Exploration