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?