The quadratic formula is a method used to solve quadratic equations, which are equations of the form:

$ax^2 + bx + c = 0$

The formula provides the solutions for $x$ as:

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

Where:

• $a$, $b$, and $c$ are coefficients from the quadratic equation.
• The expression under the square root, $b^2 - 4ac$, is called the discriminant.

Key Points:

• If the discriminant ($b^2 - 4ac$) is positive, there are two real and distinct solutions.
• If the discriminant is zero, there is exactly one real solution (a repeated root).
• If the discriminant is negative, there are two complex solutions.

Would you like more details or examples of how to use the quadratic formula? Here are five related questions:

1. How do you determine the discriminant of a quadratic equation?
2. Can the quadratic formula be used for any quadratic equation?
3. What does it mean if the discriminant is negative?
4. How do you factor a quadratic equation if the quadratic formula gives a perfect square discriminant?
5. What are the practical applications of solving quadratic equations?

Tip: Always simplify your equation to the standard quadratic form $ax^2 + bx + c = 0$ before applying the quadratic formula.