In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation. Other ways of solving quadratic equations, such as completing the square, yield the same solutions. Given a general quadratic equation of the form ax2+bx+c=0{\displaystyle \textstyle ax^{2}+bx+c=0}, with x{\displaystyle x} representing an unknown, and coefficients a{\displaystyle a}, b{\displaystyle b}, and c{\displaystyle c} representing known real or complex numbers with a≠0{\displaystyle a\neq 0}, the values of x{\displaystyle x} satisfying the equation, called the roots or zeros, can be found using the quadratic formula, where the plus–minus symbol "±{\displaystyle \pm }" indicates that the equation has two roots. Written separately, these are: The quantity Δ=b2−4ac{\displaystyle \textstyle \Delta =b^{2}-4ac} is known as the discriminant of the quadratic equation. If the coefficients a{\displaystyle a}, b{\displaystyle b}, and c{\displaystyle c} are real numbers then when Δ>0{\displaystyle \Delta >0}, the equation has two distinct real roots; when Δ=0{\displaystyle \Delta =0}, the equation has one repeated real root; and when Δ<0{\displaystyle \Delta <0}, the equation has two distinct complex roots, which are complex conjugates of each other. Geometrically, the roots represent the x{\displaystyle x} values at which the graph of the quadratic function y=ax2+bx+c{\displaystyle \textstyle y=ax^{2}+bx+c}, a parabola, crosses the x{\displaystyle x}-axis. The quadratic formula can also be used to identify the parabola's axis of symmetry.