Parabola Plotter

Author:
perspect
Topic:
Parabola
Here is the parabola plotter. Try to drag the bar to change a, b and c independently to see the change of parabola. Remember the change of it!
1. What is the locus of the vertex when a, c are fixed and b change? 2. Why is the graph a straight line when a= 0? (and why there is no vertex?) 3. How is the graph looks like when a>0, b<0 and c<0?