To solve a quadratic equation, which of the following methods can be used?

The quadratic equation can be solved through several methods, showcasing the versatility of techniques available to determine its roots. The quadratic formula is a reliable method that can be applied to any quadratic equation, regardless of whether it can be factored easily. The formula, ( ax^2 + bx + c = 0 ), provides a straightforward method to find solutions ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ).

Factoring is another effective method used when the quadratic can be expressed as a product of two binomials. This method can be particularly quick and efficient when the coefficients are simple and lend themselves to an easy factorization.

The other methods mentioned, such as completing the square and graphing, are also valid practices for solving quadratic equations, but they are not limited to more general approaches. Completing the square transforms the quadratic into a vertex form which can reveal the solutions, while graphing allows for visual interpretation of roots by identifying where the parabola intersects the x-axis.

Thus, using both the quadratic formula and factoring enables the solver to approach these equations from multiple angles, making it the most comprehensive choice among the options provided.