What is the quadratic formula used to find?

The quadratic formula is specifically used to find the roots of a quadratic equation, which is an equation that can be expressed in the standard form ( ax^2 + bx + c = 0 ), where ( a ), ( b ), and ( c ) are constants, and ( a ) is not zero. The roots, also referred to as solutions or zeros, are the values of ( x ) that make the equation true—meaning they are the points where the quadratic function intersects the x-axis.

The formula itself is given by ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ). Here, the expression under the square root, ( b^2 - 4ac ), is known as the discriminant and provides crucial information about the roots: if it's positive, there are two distinct real roots; if it's zero, there is exactly one real root (a repeated root); and if it's negative, the roots are complex.

Understanding the application of the quadratic formula is essential when solving quadratic equations, as it provides a systematic method for finding solutions regardless of the specific coefficients of ( a ), ( b ), and ( c ), as long