Quadratic Equations

What is a Quadratic Equation?

You should know by now how to associate pictorial patterns in graphs with symbolic patterns in formulas. The main associations that can be have made are summarized in Figure 1 (below).

Figure 1: Associating pictorial shapes (graphs) with arrangements of mathematical symbols (formulas).

The purpose of making these associations between graphs and formulas is to allow you to take a set of numerical data, graph it, and then create a formula that does a good job of representing what is going on.

Once you have that formula, you can make predictions about what is likely to happen and be better prepared for future events.

Examining data, creating graphs and formulas and making predictions is a way for you to gain more insight into how your world works and what the world is likely to throw at you in the future. It is very important that you learn how to use a new symbolic pattern to describe trends that either reach a low point and then rebound (see Figure 2(a)) or reach a high point and then decrease (see Figure 2(b)).