Quadratic Function Terminology

Before you start graphing quadratic functions and working with their graphs, it is important that you are familiar with the terminology associated with this topic. This page will take you through some of the basic terms that you need to know.

Parabola

The graph of a quadratic function will be a parabola. A parabola is a curve that 'changes direction' once (at the vertex). Some people say that parabolas look like 'smiles' or 'frowns'. A parabola can open upwards or downwards. Below is the graph of y = x²:

This parabola is said to 'open upward'. An important note: Parabolas will continue to get wider and wider as you move left and right on the graph (the arms never head straight up or down.)

Vertex

The vertex of a parabola is the point on the graph where the parabola 'changes direction'. It is either at the lowest point (for an upward facing parabola) or the highest point (for a downward facing parabola) of the parabola.

The pictures below show two examples of vertices (the plural of vertex) and their co-ordinates.

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It is important that you can locate the vertex as you will need to manipulate the vertex when you work with graph transformations.

Axis of Symmetry

The axis of symmetry is an imaginary straight line that runs through the vertex of the parabola and bisects (splits in half) the parabola. Pictured below are the same two parabolas from above, with the axis of symmetry drawn in as a thick red line.

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In the left graph, the equation of the axis of symmetry is x = 2. In the right graph the equation of the axis of symmetry is x = -4.

Maximum/Minimum Values

You will commonly be asked to find the 'maximum' or the 'minimum' of a parabola. This is either the y-coordinate of the lowest point (for an upward pointing parabola) or the highest point (for a downward turning parabola). The graphs below have their maximum or minimum point labelled.

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Domain and Range

Domain and range for quadratic functions work the same way as the domain and range that you have already studied. The domain of a graph is the set of all of the x-values (or coordinates) that exist in the function. The range of a graph is the set of all of the y-values (or coordinates) that exist in the function. The domain for ANY quadratic function is the set of all real numbers (ie. ). The range of a quadratic function is a little harder, as it changes depending on the function. Let's examine each graph:

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There are no sample questions for this topic. You will be tested in each lesson after this one because you have to know these terms to be able to understand what is happening. Now you can head back to the Quadratic Functions main page.