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.