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Download 101 Uses of a Quadratic Equation (KS4 workshop)
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101 uses of a quadratic equation Chris Budd Is the quadratic equation evil? And does anyone care? Babylonians Counted in Base 60 x Area ax 2 x Area x x ax bx 2 Quadratic equation ax bx c 0 2 Solutions b b 4ac x 2a 2 x 2 2 X = 1.4142135623730950488… A4 Paper Conic sections Appolonius Cone Ellipse Parabola Hyperbola Ellipse 2 Parabola 2 x y 2 1 2 p q y 4 px 2 Hyperbola 2 2 x y 2 1 2 p q All these curves obey quadratic equations How conic sections caused a revolution Copernicus Tycho Brahe Kepler Galileo Studied how things move and found that they obeyed quadratic equations Cars do ….. THUD!! .. Was the car speeding? Forensic evidence: collision damage, witness statements, skid marks s u F distance of skid speed brake force Quadratic equation links them together Solving the equation gives the speed 2 u s 2F u 2 Fs So do rugby balls …. y bx ax Parabola 2 Sir Isaac Newton Explained the link and also invented the reflecting telescope based on the parabola Newton discovered differential equations 2 d u du a 2 b cu 0 dt dt Used to explain almost everything • Pendulums • Car suspensions • Musical instruments • Radios and TV Euler finds the solution ue xt ax bx c 0 2 Solve the quadratic equation to solve the differential equation And millions of important problems Quadratic equations take flight u 2 2 P gh Speed Pressure Bernouilli Chaotic quadratic equations Bee population x evolves every year xnew a xold (1 xold ) population a=2 Population settles down population a=3 Boom and bust population a=4 Chaos Are you still frightened of me?
