What is the quadratic formula used to find?

The quadratic formula is specifically designed to find the zeros (or roots) of a quadratic function, which is represented in the standard form as ( ax^2 + bx + c = 0 ). The formula itself is expressed as:

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

]

In this context, the term "zeros" refers to the values of ( x ) that make the quadratic function equal to zero. Identifying these points is essential in various applications, such as determining where a parabola intersects the x-axis, which can inform decisions in business and social sciences.

The other options reflect different properties of a quadratic function. The leading coefficient is related to the shape and direction of the parabola but does not provide the roots. The degree of a quadratic function is always two, indicating that it is a second-degree polynomial, which does not involve solving for ( x ). The vertex of a quadratic function represents the maximum or minimum point of the parabola, which can be located using other methods, but is not what the quadratic formula directly provides. Therefore, the correct choice highlights the primary purpose of the quadratic formula in finding the zeros of a quadratic function