What is the quadratic formula used for finding?

The quadratic formula is specifically designed to find the solutions of a quadratic equation, which is represented in the standard form as ( ax^2 + bx + c = 0 ). The formula is given by

[

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

]

where ( a ), ( b ), and ( c ) are coefficients in the quadratic equation, and the term ( b^2 - 4ac ) is known as the discriminant. The quadratic formula allows us to determine the values of ( x ) that make the equation true, which can indicate the points where the corresponding parabola intersects the x-axis. This makes it a powerful tool in algebra for solving quadratic equations.

The other choices do not pertain to the quadratic formula. For example, calculating the square root of a number is a different mathematical operation requiring a separate approach. The area of a circle is determined using the formula ( A = \pi r^2 ), unrelated to quadratic equations. Similarly, the slope of a line, found using the formula ( \text{slope} = \frac{y_2 - y_1}{x_2 - x