Today’s soundtrack is Liquid Tension Experiment: Liquid Tension Experiment, an experimental progressive instrumental rock album by some of the members of Dream Theater (and friends).
This afternoon, I’m working on [what I hope will be] the last part of this lesson about the vertex form of the quadratic formula. Links to previous sessions: part 1, part 2, and part 3.
I figured out today that we can use the vertex form of a quadratic function to determine the number of xintercepts the graph will have, because a tells us which way the graph opens, and q tells us the yaxis of the vertex. By using a and q, we can analyze it just on sight like this:

If a > 0 and q > 0, there will be no xintercepts

If a > 0 and q < 0, there will be two xintercepts

If a < 0 and q < 0, there will be no xintercepts

If a < 0 and q > 0, there will be two xintercepts

If q = 0, there will be one xintercept
And with that, I’m finally done this chapter!