What is the quadratic formula used for?

The quadratic formula is specifically designed to solve quadratic equations, which are polynomial equations of the form ax² + bx + c = 0, where a, b, and c are constants and a is not equal to zero. The formula provides a method to find the values of x that make the equation true, which are known as the roots of the quadratic equation. It is expressed as x = (-b ± √(b² - 4ac)) / (2a). This formula is essential for determining the points where the parabola represented by the quadratic equation intersects the x-axis, which corresponds to the solutions of the equation.

The other options deal with different mathematical concepts: linear equations relate to first-degree equations, the area of a triangle involves different geometric calculations, and the slope of a line is derived from linear relationships, none of which require or relate to the quadratic formula.