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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
x
x
x Area
Area
2ax
bxax 2
02 cbxax
a
acbbx
2
42
Quadratic equation
Solutions
X = 1.4142135623730950488…
22 x
A4 Paper
Conic sections
ConeAppolonius
Ellipse
Parabola
Hyperbola
Ellipse Parabola Hyperbola
All these curves obey quadratic equations
1412
2
2
22
2
2
2
2
q
y
p
xpxy
q
y
p
x
How conic sections caused a revolution
Copernicus
Tycho BraheKepler
Galileo
Studied how things move and found that they obeyed quadratic equations
Cars do …..
..
Was the car speeding?
Forensic evidence: collision damage,
witness statements,
skid marks
THUD!!
Fsu 2
F
us2
2
s distance of skid
u speed
F brake force
Quadratic equation links them together
Solving the equation gives the speed
Parabola
So do rugby balls ….
2axbxy
Sir Isaac Newton
Explained the link and also invented the reflecting telescope based on the parabola
02
2
cudt
dub
dt
uda
Newton discovered differential equations
Used to explain almost everything
• Pendulums
• Car suspensions
• Musical instruments
• Radios and TV
Euler finds the solution
xteu
02 cbxax
Solve the quadratic equation to solve the differential equation
And millions of important problems
Quadratic equations take flight
ghPu
2
2
SpeedPressure Bernouilli
Chaotic quadratic equations
Bee population x evolves every year
)1( oldoldnew xxax
a = 2 Population settles down
population
a = 3 Boom and bust
population
a = 4 Chaos
population
Are you still frightened of me?
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