Final answer:
The quadratic formula is used to find the solutions of quadratic equations, which are in the form ax² + bx + c = 0. It's particularly useful when the equations cannot be factored easily.
Step-by-step explanation:
The quadratic formula is a method used to find the solutions to quadratic equations, which are mathematical functions also known as second-order polynomials. For an equation in the form ax² + bx + c = 0, where a, b, and c are constants and a is not equal to zero, the solutions can be calculated using the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
We use the quadratic formula when a quadratic equation cannot be easily factored or is not a perfect square. It provides a straightforward technique to solve for x, giving us the roots or solutions to the equation. Since quadratic equations often represent real-world scenarios, such as projectile motion, the formula is frequently used in such applications to find real roots, which can have significant physical interpretations.