Sam Ventresca, Carla Marano, Lore Baruwa The Quadratic Formula Sam Ventresca, Carla Marano, Lore Baruwa

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 Al- Khwarismi around 820 circa Baghdad. Brahmagupta’s Formula

History of Quadratic Formula: Italy In1545, Girolamo Cardano compiled Al- Khwarismi’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 semi- conductors, 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-quadratic- equation-part-ii