The Quadratic Formula by Zach Barr Simulation Online

The Quadratic Formula by Zach Barr

Simulation Online

History of Quadratic Formula § § A quadratic equation is a second order, univariate polynomial with constant coefficients and can usually be written in the form: ax^2 + bx + c = 0, where a cannot equal 0. In about 400 B. C. the Babylonians developed an algorithmic approach to solving problems that give rise to a quadratic equation. This method is based on the method of completing the square. Quadratic equations, or polynomials of second-degree, have two roots that are given by the quadratic formula: x = (-b +/- (b^2 - 4 ac))/2 a. The earliest solutions to quadratic equations involving an unknown are found in Babylonian mathematical texts that date back to about 2000 B. C. . At this time the Babylonians did not recognize negative or complex roots because all quadratic equations were employed in problems that had positive answers such as length. § 1. 2. For more information about the history of the Quadratic Formula, visit these two sites The Original Problem Babylonians

Deriving the Quadratic Formula § To derive the equation x^2 + bx + c = 0 into the quadratic formula, you must complete the square as shown on the webpage.

What is the formula used for? § The Quadratic Formula is used to find the zeroes of an equation. § X represents the variable that we are trying to find. Because the equation is a second-order polynomial equation, with the term x^2, there will be two solutions.

What to do? § § § Given equation: a, b, c are coefficients for the equation Substitute in each value of a, b, c into the quadratic formula and solve for x. § Note: Remember the + OR – in front of the square root sign. This is how you get your two answers as you will see later.

Example: § For this equation: a=1, b=2, c=-8 § Use Quadratic formula: § Plug in a, b, c to get:

Continuing Example § Solve: OR OR OR

§ § Use a graphing calculator to graph the equation x^2 +2 x-8=0. From the look of the graph, we find that the same two zeroes x=2, -4 as we did using the quadratic formula.

The End! By Zach Barr 9/26/2005