Use this Exploration of Quadratic Function using sliders to explore the relationships between factors and roots/zeros.

Does Y_3 always correspond to the y-intercept of f(x)?
Explore and understand when it does and when it does not and why this is happening. Can you come up with a strategy to make it so that it always corresponds?
Do the points (sym + sqrt(disc) / (2a), 0) and (sym - sqrt(disc) / (2a), 0) always correspond to the x-intercepts of f(x)?
Explore and understand when it does and when it does not and why this is happening.
Shift your sliders to a = 1, b = 2, and c = 5. Solve the quadratic using either completing the square or the quadratic formula. Compare your result to what you see on GeoGebra.
Explain what the points D and E (if-then points) represent and why that makes sense given what we did to create the points.