A Quadratic Equation looks like this: And it can be solved using the Quadratic Formula: That formula looks like magic, but you can follow the steps to see how it comes about. 1. Complete the Squareax2 + bx + c has "x" in it twice, which is hard to solve. But there is a way to rearrange it so that "x" only appears once. It is called Completing the Square (please read that first!). Our aim is to get something like x2 + 2dx + d2, which can then be simplified to (x+d)2 So, let's go:
Now x only appears once and we are making progress. 2. Now Solve For "x"Now we just need to rearrange the equation to leave "x" on the left
Copyright © 2017 MathsIsFun.com
The “horrible looking” quadratic formula below
is actually derived using the steps involved in completing the square. It stems from the fact that any quadratic function or equation of the form y = a{x^2} + bx + c can be solved for its roots. The “roots” of the quadratic equation are the points at which the graph of a quadratic function (the graph is called the parabola) hits, crosses or touches the x-axis known as the x-intercepts. So to find the roots or x-intercepts of y = a{x^2} + bx + c, we need to let y = 0. That means we have a{x^2} + bx + c = 0 From here, I am going to apply the usual steps involved in completing the square to arrive at the quadratic formula. Steps on How to Derive the Quadratic FormulaDerivation of the quadratic formula is easy! Here we go.
I hope that you find the step-by-step solution helpful in figuring out how the quadratic formula is derived using the method of completing the square. You might be interested in: The Quadratic Formula |