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101 uses of a quadratic equation Chris Budd

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Is the quadratic equation evil? And does anyone care?

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Babylonians Counted in Base 60

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x x x x Area Area

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Quadratic equation Solutions

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X = 1.4142135623730950488… A4 Paper

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Conic sections Cone Appolonius

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Ellipse

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Parabola

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Hyperbola

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Ellipse Parabola Hyperbola All these curves obey quadratic equations

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How conic sections caused a revolution

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Copernicus

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Tycho Brahe Kepler

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Galileo Studied how things move and found that they obeyed quadratic equations

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Cars do ….... Was the car speeding? Forensic evidence: collision damage, witness statements, skid marks THUD!!

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s distance of skid u speed F brake force Quadratic equation links them together Solving the equation gives the speed

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Parabola So do rugby balls ….

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Sir Isaac Newton Explained the link and also invented the reflecting telescope based on the parabola

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Newton discovered differential equations Used to explain almost everything Pendulums Car suspensions Musical instruments Radios and TV

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Euler finds the solution Solve the quadratic equation to solve the differential equation And millions of important problems

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Quadratic equations take flight Speed Pressure Bernouilli

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Chaotic quadratic equations Bee population x evolves every year

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a = 2 Population settles down population

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a = 3 Boom and bust population

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a = 4 Chaos population

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Are you still frightened of me?

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Section 9.1 Quadratic Functions and Their Graphs.

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