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.

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 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 forCompleting 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.