Students drag the expression x2 to the x axis to display the graph of the function y = x2. Ask them to describe the shape of the graph. Be sure to mention that this curve is called a parabola.

Moving the cursor near the vertex of the parabola. Have the students observe the changes in the equation. Explain that the equation is written in what is called the vertex form of a quadratic equation: y = a(x   h)2 + k. For now, students will look at functions for which a = 1.

As they more the parabola, have them pay attention to the changing value of h.

Discuss that when the graph opens downward (when a is negative), the vertex is a maximum because it is the highest point on the graph.      
They can now display the equation of the axis of symmetry by using the Coordinates and Equations tool. Allow time for students to move and change their parabolas, observing how the equation changes with it. Circulate around the room and assist as needed.    

Once students understand how an equation in vertex form is related to the graph of the function, they can sketch the graphs of the three functions shown on their worksheet. Stress that this is only a sketch, and will not be exact, although they should be able to place the location of the vertex exactly. While they should know the direction of the parabola (up or down) from a, the exact width should be an educated guess.