# Modeling

In our earlier discussion when we talked about finding the equation of a parabola, all of the methods we used required parabola-centric pieces of information, e.g. the location of the vertex or the directrix or the focus. In this lecture, we're going to talk about how to find a parabola's equation, i.e. a quadratic equation, based just on knowing the coordinates of points that are on it.

# Video Lectures

An important practical question that shows up in multiple real world situations and mathematical fields is, "What's the optimal value for this situation?" In other words, what values of the variables give the best results. Using our vertex formula, we can answer that question for situations that can be modeled using quadratic polynomials. In this lecture, we're goint to look at two theoretical results then, in the next one, we'll switch directions and look at practical applications.

In this lecture, we'll see how to apply the theoretical results from the previous lecture to practical situations and how to handle practical scenarios where the theoretical results don't apply.