Vertex Investigation

This sketch helps you investigate the location of the vertex for a parabola in standard form, y=ax^2+bx+c. Since the equation will tell us y if we know x, we will concentrate on the x-coordinate of the vertex. 1) There are controls for a and b, separate from c. Why doesn't c change the left-right location of the vertex? 2) Change a and b and notice the effect on whether the vertex moves left or right. What do you notice? 3) Our goal is to find a rule or frmula for the vertex's x-coordinate in terms of a and b. How can you collect data that will help us determine the formula? Extension: what else could you investigate with this sketch?