Babylonian mathematicians as early as the Sumerian Ur III period (21st to 20th century B.C.) used geometric methods to solve second-degree problems. Similar geometric methods solved quadratic equations in later Babylonia, Egypt, Greece, China, and India. Indian mathematician Brahmagupta (597-668 C.E.) was the first to give an explicit solution.Know More
Ancient Babylonians understood second-degree equations as geometric problems of sides and areas of rectangles and squares. The equation can be geometrically stated as saying that if a rectangle with sides of the length s and f/2 * s is removed from a rectangle with sides p and s, then the remainder is a rectangle of given area B. Euclid summarized these geometric solutions in Book II of the Elements where he represented such problems by a combination of rectangles and lines.
Brahmagupta of India was instrumental in understanding that numbers are abstract concepts which can be zero or negative. He pointed out that quadratic equations can have two possible solutions, one of which can be negative. He derived algebraic solutions to quadratic equations and went several steps further by solving systems of equations and quadratic equations with two unknowns. The latter was not considered by European mathematicians until more than a millennium later.Learn more about Algebra
Solve quadratic equations by graphing, using square roots, factoring, completing the square or using the quadratic formula. Determine the most appropriate method by considering the particular situation.Full Answer >
A quadratic function is a function of the form f(x) = ax^2 + bx + c where a, b and c are constants. Part of the definition of a quadratic function is that a is not equal to zero, although b and c can equal zero.Full Answer >
The simplest way to graph a quadratic equation is to substitute an array of values for x in the equation and solve for y in each case to obtain several (x,y) coordinates. After obtaining the coordinates, they can be plotted on graph paper along the x-y axis to form a parabolic curve that is typical of a quadratic equation.Full Answer >
Plot at least seven points from the quadratic equation, and then draw a parabolic curve through the points to make the graph. Remember that quadratic equations always show up as parabolas on graphs.Full Answer >