Lines are simple and they serve a good approximation for getting from one point to the next.
Quadratics are a little more complex, but still approachable with by-hand arithmetic as well as allowing for a little more complicated algebra in analyzing them. They represent going up and then coming down, or the reverse. That is, these are the hills and valleys.
We can solve quadratic equations with iterative guessing, inspired algebraic manipulations, or formulas. We will explore them and then do a variety of applied examples to see how each technique works out.