Equation Breakdown
Where a, b, and c are the constants from any quadratic
function:
ax2 + bx + c = 0.
Prevailing View Prior to
Discovery
Before the quadratic
formula, astronomy was
largely a mystery. Without
being able to predict how
the planets rotated around
the Sun, and their
accelerations, it was
believed that the sky
rotated and the Earth was
stable.
History of Quadratic
Formula: Egypt
Egyptians in 1500 BCE
didn’t create equations,
but created tables of
area values for all
shapes based on any
side length.
History of Quadratic
Formula: Babylonia
Around 400 B.C,
Babylonians discover
the concept of
“completing the
square”.
History of Quadratic
Formula: Greece
Circa 300 BCE, Greek
philosopher Euclid
discovers that
irrational numbers
exist based on work of
Pythagoras
History of Quadratic
Formula: Circa Baghdad
In 700 AD, Brahmagupta
developed quadratic
equation and recognized
two roots, and derived
independently by
Mohammad bin Musa AlKhwarismi around 820
circa Baghdad.
Brahmagupta’s Formula
History of Quadratic
Formula: Italy
In1545, Girolamo
Cardano compiled AlKhwarismi’s ideas with
Euclidian geometry. This
allowed for the existence
of imaginary roots, or
roots of negative
numbers.
History of Quadratic
Formula: France
In 1637, René Descartes
published La Géometrié.
Essentially the birth of modern
mathematics, and the
quadratic formula was
developed here in the way we
know today. Quadratic formula
is derived from completing the
square of ax2 + bx + c = 0.
Societal Impact of Quadratic
Formula: Business
Since the quadratic
equation is the prominent
equation of supply and
demand, the quadratic
formula is useful in
business and economic
applications to find roots
that do not factor
perfectly.
Societal Impact of
Quadratic Formula: Space
When Kepler discovered that
the Earth’s orbit was, in fact, an
ellipse, it opened the door for
quadratic equations to predict
this orbit more precisely.
In the 17th century, Galileo ,
noticed this equation could be
used to determine the
acceleration of planets around
the Sun.
Societal Impact of Quadratic
Formula: Cell Phones
The quadratic formula lead to the
discovery of imaginary numbers,
which lead to the fundamental
quantum theory.
This equation allows one to predict
the motion of electrons in semiconductors, which make it possible
to design integrated circuits. These
circuits are the base of most
modern technology, including cell
phones.
Works Cited
• http://www.purplemath.com/modules/quadform.htm
• http://h2g2.com/dna/h2g2/A2982567
• http://www.purplemath.com/modules/sqrquad2.htm#
formula
• http://neohumanism.org/q/qu/quadratic_formula.html
• http://plus.maths.org/content/101-uses-quadraticequation-part-ii