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. |
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| 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. |
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| The discriminant - Advanced applications - Test Yourself 1 - Solutions. |