What is the quadratic formula used for in mathematics?

The quadratic formula is specifically designed to find the roots of quadratic equations, which are equations of the form ax^2 + bx + c = 0. By applying the quadratic formula (x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}), you can determine the values of x that make the equation true. This formula provides a systematic method for solving any quadratic equation, whether the roots are real or complex, making it a foundational tool in algebra and higher-level mathematics.

The other options do not accurately describe the function of the quadratic formula. Factoring polynomials is a different technique used to break down expressions into simpler components. The area of a triangle involves geometry and specific formulas like (A = \frac{1}{2} \times \text{base} \times \text{height}), rather than the quadratic formula. Lastly, graphing linear equations pertains to a different set of algebraic principles, typically involving first-degree equations rather than the second-degree equations that the quadratic formula addresses.