Families of Graphs are graphs that look alike but vary by some variable (called a parameter). For example, linear equations are all straight lines, but you can change the slope and y-intercept parameters. The Families Of Graphs Applet allows a user to investigate "parameterized families of graphs" by changing the value of one or more parameters. You can play with the parameters by moving the sliders on the bottom of the graphs.
The applet below shows the quadratic equation y = a(x + h)^2 + k. Examine what happens to the graph if we change the value of h (inside the parenthesis), or k (outside the parenthesis).
The next applet shows the linear equation y = 2x + 3. Examine what happens to the graph if we change the slope, m, or the y-intercept, b.
The last graph includes an example from trigonometry, an absolute value function, a rational function, and one more form of a quadratic function. Select other examples from the pull-down menu at the top of the applet and click the "Load Example" button.