A **polynomial** equation of second degree (i.e. *x*²) is called a **quadratic equation**. It is common practice to refer to it simply as a **quadratic**.

A quadratic is in *general form* when it is written in the following form, where *a*, *b*, and *c* are constants:

y = **a**x² + **b**x + **c**

The graph of a quadratic relation is called a **parabola**. A parabola has a **minimum** point or a **maximum** point called the **vertex**. It is also symmetrical about a vertical line drawn through the vertex, called the **axis of symmetry**. Examples of parabolas are shown underneath.

Before we learn the techniques to graphing quadratics, let’s start by creating a table of values for a quadratic function. Eventually as we become more familiar with quadratics, we can ditch the usage of a table and rely strictly on key features found in the equation itself.

The video below demonstrates how to use a table of values to produce a parabola. Notice how the **a**-term dictates whether the parabola faces up like a smile **∪** or faces down like a frown **∩**.

Now that you have an idea how to graph a quadratic using a table of values. This next video will show you how you can use the idea of **first differences** to determine from a table if it represents a quadratic or linear equation.

Moving forward, remember the following two things:

- A parabola is symmetric about a vertical line that passes through the vertex. This line is the axis of symmetry.
- If a relation is quadratic, the second differences are constant, but the first differences are not.