Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

Functions - non-linear - Quadratics.


The parabola is a very important function in Mathematics and its shape is easily recognised - although there are apparently some people who do not know its name as a "parabola". You will see a number of parabolic shapes in the introduction video.

The equation of a parabola is referred to as being a quadratic equation. It is characterised as having a term in y and a term in x2 (or the reverse - a term in x and a term in y2) and possibly other terms with lower indices. So the highest power or index for the independent variable in a quadratic equation is always 2 - and we refer to this feature of the highest power as being the degree of the equation. So we can say that a quadratic equation is of degree 2.

The degree of 2 separates the quadratic equation from other families of curves - for example from a cubic equation
of the form y = x3 (which is therefore an equation of degree 3).

The resources relating to the quadratic function which are accessed from this page are:

1. Introduction to the parabola and its applications.
2. A comparison between the parabola and the similar shaped catenary.
3. Drawing parabolas.
4. The quadratic formula.
5. The discriminant.


Topic Evaluation
1. Introduction to the parabola. Video
2. Comparison between the Parabola and the Catenary. Web page.
3. Drawing parabolas. Review of drawing parabolas.
  Drawing parabolas - Test Yourself 1.
  Drawing parabolas -
Test Yourself 1 - Solutions.
Review (if required):
The factorisation technique for
Completing the Square.
4. The Quadratic formula. Video coming soon
  Test Yourself - Test 1.
  Solutions to Test Yourself 1.
5. The discriminant. The discriminant - basic skills and applications -Test Yourself 1.
  The discriminant - basic skills and applications -Test Yourself 1 - Solutions.
  The discriminant - Advanced applications -
Test Yourself 1.
  The discriminant - Advanced applications -
Test Yourself 1 - Solutions.