WolframAlpha

Type in, for example, an equation you want to solve, a function you want to graph or the names of two cities. You will want to keep playing. This video by Robert Talbert gives some ideas about how a math teacher or student might begin exploring.

Vertical Motion Simulation

This GeoGebra applet by Linda Fahlberg-Stojanovska simulates the motion of a projectile fired either straight up or straight down on Earth in the absence of air resistance. The user sets the initial height and the initial velocity and indicates whether units of measure should be feet or meters. You see the motion of the ball along the vertical axis, while the height as a function of time is plotted for you.

Graph of a quartic

In this GeoGebra applet, you graph a quartic by setting the values of the four zeros and the leading coefficient. The coordinates of all relative extrema are shown.

Visualizing the dot product

Mystery Vector Function is a GeoGebra applet I created to introduce students to the dot product. In this applet, students observe a rectangle in which the length of one side is equal to the magnitude of vector b and the length of other side is equal to the projection of vector a onto b. They discover that the signed area of this rectangle is equal to the product of the magnitude of a, the magnitude of b, and the cosine of the angle between them. They can then use the angle difference identity for cosine to show that this is equal to the sum of the product of the x-components and the product of the y-components.

Modeling with sine and cosine

In this applet, you look at the graph of a data set (for water level in Cape May, NJ on October 13, 2009) and try to fit a sine function and a cosine function to the data. You can type in your function to see how well it fits the data. Some instruction on how to determine the parameters is provided.

Writing Equations for Sine and Cosine Functions

This applet I created with GeoGebra has 40 problems, which get progressively more difficult, in which the student must write an equation for a graph which is a stretch and/or translation of a sine/cosine graph. To check whether an equation is correct, the student types in the equation and looks at whether the graphs match up.

Finding the equation of a parabola

This is an applet I created using Geogebra in which the user is asked to enter the equation of randomly generated parabola. The equation entered is graphed for comparison to the target parabola.