Use the sliders that control coefficients a, b and c to move the parabola. Can you predict where the vertex and axis of symmetry will be?
After playing around for a minute or two, try to only change one of the coefficients at a time. What does the a coefficient do to the curve? What does the c coefficient do to the curve? What does the b coefficient do to the curve? What is the equation of the axis of symmetry? What formula can you come up with to predict where the axis of symmetry will be?