Before You Watch

This video demonstrates how to solve a particular type of equation called a quadratic equation.
To get the most out of this topic, you'll need to be comfortable with the rearrangement of algebraic equations, as well as indices as they are applied to algebra. If you need to brush up on your skills in these areas, take a look at the Introduction to Algebra and Indices Laws videos first, then come back.

The Video

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Some Practice Questions

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Now What?

You may find it helpful to follow through and see how the quadratic formula is created. You can see the derivation in the Maths Is Fun website at http://www.mathsisfun.com/algebra/quadratic-equation-derivation.html. ]. It is not necessary to know this derivation, but it might assist your understanding. Another option for watching the derivation of the quadratic formula is the video by PatrickJMT at http://patrickjmt.com/deriving-the-quadratic-formula/ .

Now that you're familiar with the use of the quadratic equation, why not check your skills in some of the areas covered by the other algebra videos? Factorisation of Algebraic Expressions  is particularly relevant to the alternative method of solving quadratic equations. Others such as Algebraic Fractions and Simultaneous Equations will also help develop your abilities in algebra.

But When I am Going to Use This

Quadratic equations are very important as they are useful in understanding situations such as movement under constant acceleration (like gravity), a thrown ball if we ignore wind resistance, or pendulums or weights on springs. In fact, the quadratic equation is the base level solution for all stable systems, so it's one of the most widely studied systems in physics and engineering. Some stable systems that are often approximated using a quadratic equation include an atom’s position in a molecule or solid, a thermostat attempting to maintain a constant temperature, or even a child on a swing.

Other Links

As well as showing the derivation of the quadratic formula, Maths Is Fun has a great applet where you can enter the formula for any quadratic equation. It then graphs the corresponding parabola for that quadratic and solves it for you. This is useful because it helps you visualise the solutions to the quadratic as positions on a parabola. However, keep in mind that you will still need to be able to solve the quadratic equation yourself.

It also has worked solutions and sample questions here:

The Mathportal website has another great applet to help you develop your understanding of the quadratic equation and how to solve it. It allows you to input any quadratic equation, and it will show you a worked step-by-step solution to that equation using either the quadratic formula, or another method known as completing the square.

The Khan Academy has a comprehensive set of video tutorials covering a large range of mathematical and other concepts, as well as questions to test your knowledge. It has a chapter dedicated to solving quadratic equations using the formula. This includes eight videos and a summarising test at the end.

Patrick JMT (Just Maths Tutorials) has a comprehensive set of video tutorials covering a large range of mathematical concepts. Here are two videos relevant to this topic: the first covers the use of the quadratic formula, and the second is the first in a series of videos showing example questions.