What is the quadratic formula used for?

The quadratic formula is specifically designed to find the roots of quadratic functions, which are equations of the form (ax^2 + bx + c = 0). This formula states that the solutions (x) can be found using the expression

[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a}

]

In this formula, (a), (b), and (c) are the coefficients of the quadratic function. The roots of a quadratic function are the values of (x) where the function equals zero, and these points are significant because they help in understanding the behavior of the graph of the quadratic function.

The correct answer focuses on the primary application of the quadratic formula, which is crucial for solving quadratic equations and determining where their graphs intersect the x-axis (the roots). This contrasts with the other options, which reference concepts that are unrelated to the direct application of the quadratic formula.