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Quadratic Equation Calculator

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Quadratic Equation Calculator

Some of us know them with affection, others only see fear and loathing in the tricky little blighters, but one thing is for sure, quadratic equations come up time and again at school and in life, often just when you never expected them.

When a projectile is cast into the air, for example a stone being thrown or a cannon ball being shot, the path it takes forms a parabola. Quadratic equations can be used to describe such paths. In fact, if gravity is involved, quadratic equations are likely to be there too. They can be involved in a wide number of everyday and not-so usual things, from describing the path of a kicked football to the moon landing.

The shape of a parabola created by a quadratic equation can be used in a parabolic satellite receiver or a radio telescope where the shape helps to concentrate signals at a certain point. Parabolas can be used to support architecture like bridges, buildings and other structures, and can even describe the path of a water fountain.

Quadratic equations can be used to create amazing beauty too in the form of fractals. The Julia set and Mandelbrot set of fractals, which can be explored in so much depth and wonder, depend on quadratic equations for their creation.

Use our Quadratic calculator to quickly find the solutions to any quadratic equation. Remember, if you're using this for school homework, you'll need to give your workings to show how you arrived at the answers. Think of mathematics as a journey along a path to a final destination. The calculator will indicate where your journey should end. Showing the routeway is your task to enjoy.

Quadratic Equations are written in the format ax²+bx+c=0. Complete a quadratic equation using the yellow boxes (an example of 23x²+78x-37=0 has been entered initially as an example), then click the Calculate button to show the solutions in the green boxes.

x²+ x+ =0

The area bounded by the curve above the x-axis is: sq. units.
The gradient of the curve at any point is: .
The value of the curve occurs at co-ordinates: .

History of Quadratic Equations

The history of quadratic equations can be traced back to evidence left by ancient Babylonians in clay tablets. Around the 8th century BC in ancient India the Indian mathematic Baudhayana wrote a book about geometrical rules for construction and arrangement of altars. He used quadratic equations of the form shape ax² = c and ax² + bx = c, indicating methods to solve them.

Around 400 BC Babylonian mathematicians used a method known as "completing the square" to solve several quadratic equations with positive roots, but they did not obtain a general formula. Euclid described a more abstract geometric method around 300 BC. A mathematical text called the Bakshali Manuscript, written in India between 200 B.C. and 400 AD developed the solution of quadratic equations further using algebra.

In 9th Century Arabia, Al-Khwarizmi independently developed a set of formulas which worked where the answers were positive numbers. A full solution to quadratic equations was first introduced in Europe by Abraham bar Hiyya Ha-Nasi (known also with the Latin name Savasorda) with his book on algebra and geometry known as the Liber embadorum in 1145 AD.

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