This is a simple applet which aims to help students think about what happens to the graph of a quadratic as the values of the coefficients are varied.
Some possible tasks:
- Explore what happens to the graph as each of the sliders is changed. Which features of the graph change and which remain the same?
- Predict what will happen to the position of the vertex as each slider value is changed in turn. The vertex, A, can be revealed and it's locus traced as the slider is varied. This can be used to test student conjectures.
If you set the three sliders to a particular default setting you could then ask questions such as these below which will encourage students to make connections between the graphical and algebraic representations of the quadratic:
- Change one slider so that the graph touches the x-axis.
- For what range of values for a, b and c does the graph have 2 real roots?
- Change one slider so that the graph appears in one (?!), two, three or four quadrants
