Quadratic Formula
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A Quadratic Formula is an algebraic solution to a quadratic equation.
- Example(s):
- [math]\displaystyle{ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} }[/math].
- See: Factorization, Completing The Square, Graph of a Function, Constant Term, Zero of a Function.
References
2014
- (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/Quadratic_formula Retrieved:2014-10-25.
- In basic algebra, the quadratic formula is the solution of the quadratic equation. There are other ways to solve the quadratic equation instead of using the quadratic formula, such as factoring, completing the square, or graphing. Using the quadratic formula is often the most convenient way.
The general quadratic equation is [math]\displaystyle{ ax^2+bx+c=0. }[/math] Here x represents an unknown, and a, b, and c are constants with a not equal to 0. One can verify that the quadratic formula satisfies the quadratic equation, by inserting the former into the latter. Each of the solutions given by the quadratic formula is called a root of the quadratic equation.
- In basic algebra, the quadratic formula is the solution of the quadratic equation. There are other ways to solve the quadratic equation instead of using the quadratic formula, such as factoring, completing the square, or graphing. Using the quadratic formula is often the most convenient way.
2019
- (Wikipedia, 2019) ⇒ https://en.wikipedia.org/wiki/Quadratic_formula Retrieved:2019-12-26.
- In elementary algebra, the quadratic formula is a formula that provides the solution(s) to a quadratic equation. There are other ways of solving a quadratic equation instead of using the quadratic formula, such as factoring (direct factoring, grouping, AC method), completing the square, graphing and others. Given a general quadratic equation of the form : [math]\displaystyle{ ax^2+bx+c=0 }[/math] with [math]\displaystyle{ x }[/math] representing an unknown, [math]\displaystyle{ a }[/math] , [math]\displaystyle{ b }[/math] and [math]\displaystyle{ c }[/math] representing constants with [math]\displaystyle{ a \ne 0 }[/math], the quadratic formula is: :[math]\displaystyle{ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\ \ }[/math] where the plus-minus symbol "±" indicates that the quadratic equation has two solutions. Written separately, they become: : [math]\displaystyle{ x_1=\frac{-b + \sqrt {b^2-4ac}}{2a}\quad\text{and}\quad x_2=\frac{-b - \sqrt {b^2-4ac}}{2a} }[/math] Each of these two solutions is also called a root (or zero) of the quadratic equation. Geometrically, these roots represent the [math]\displaystyle{ x }[/math] values at which any parabola, explicitly given as [math]\displaystyle{ y = ax^2 + bx + c }[/math] , crosses the [math]\displaystyle{ x }[/math] -axis. As well as being a formula that yields the zeros of any parabola, the quadratic formula can also be used to identify the axis of symmetry of the parabola, and the number of real zeros the quadratic equation contains.