Quadratic Relations

A polynomial equation of second degree (i.e. x²) 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 = ax² + bx + 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.