Quadratic formula

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.

The quadratic function y = 1/2x25/2x + 2, with roots x = 1 and x = 4.

Given a general quadratic equation of the form

whose discriminant is positive (with x representing an unknown, a, b and c representing constants with a ≠ 0), the quadratic formula is:

where the plus–minus symbol "±" indicates that the quadratic equation has two solutions.[1] Written separately, they become:

Each of these two solutions is also called a root (or zero) of the quadratic equation. Geometrically, these roots represent the x-values at which any parabola, explicitly given as y = ax2 + bx + c, crosses the x-axis.[2]

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,[3] and the number of real zeros the quadratic equation contains.[4]


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