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:<math>\frac{\mathrm{d}y}{\mathrm{d}x} = 2ax + b</math>
:<math>\frac{\mathrm{d}y}{\mathrm{d}x} = 2ax + b</math>
==History==
Quadratic equations have been known about for thousands of years. The earliest known solution to a quadratic equation is often credited to the [[Babylonians]] from Berlin papyrus from the Middle Kingdom in Egypt and dated to around 2160-1700 BC.<ref name=wolfram>{{cite web|url=http://mathworld.wolfram.com/QuadraticEquation.html|title=Quadratic Equation|accessdate=2019-07-29|publisher=mathworld.wolfram.com}}</ref> However, the Babylonians did not have the concept of an equation and they only considered positive solutions as solutions normally referred to a length.<ref name=st-and>{{cite web|url=https://www-history.mcs.st-and.ac.uk/HistTopics/Quadratic_etc_equations.html|title=Quadratic, cubic and quartic equations|accessdate=2019-07-29|publisher=www-history.mcs.st-and.ac.uk|date=February 1996}}</ref> The [[Ancient Greece|ancient Greeks]] are known to have solved quadratic equations using [[geometry]]. [[Euclid]] described three problems described by quadratic equations in his ''Data'' and developed such a geometric approach in around 300 BC. Like with the Babylonians, it too only admitted positive solutions.
Several [[Indian]] mathematicians advanced ideas developed by the Babylonians. In the seventh century, a mathematician named Brahmagupta produced an almost modern method that allows for negative solutions.<ref name=st-and/> Brahmagupta also recognized that quadratics always have two solutions.<ref name=mathsnasium>{{cite web|url=https://www.mathnasium.com/the-history-behind-the-quadratic-formula|title=The History Behind The Quadratic Formula|accessdate=2019-07-29|publisher=mathsnasium.com}}</ref> Indian mathematics also developed the concept of negative numbers and zero which allowed a more complete understanding of such equations. The works of other Indian mathematicians at this time suggest they may have had an understanding of quadratic equations, though didn't explicitly describe them.<ref name=wolfram/>
A century later in 820&nsbp;AD, the Arabic mathematician Al-Khwarismi developed an understanding of quadratic equations and a formula for solving them but rejected negative solutions.
Later in 1545, Girolamo Cardano compiled all that was known about quadratic equations at the time into a single work. He suggested the existence of [[imaginary number]]s and [[complex number]]s. In the late 16<sup>th</sup> century, François Viète introduced the modern mathematical notation used for quadratics.
==Solving quadratic equations==
==Solving quadratic equations==