The quadratic formula is used to find the solutions (or roots) of a quadratic equation of the form:

$ax^2 + bx + c = 0$

The quadratic formula is:

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

Here:

• $a$, $b$, and $c$ are the coefficients of the quadratic equation.
• The symbol $\pm$ indicates that there are two solutions: one using the plus sign and one using the minus sign.
• The term under the square root, $b^2 - 4ac$, is called the discriminant. It determines the nature of the roots:
  • If $b^2 - 4ac > 0$, there are two real roots.
  • If $b^2 - 4ac = 0$, there is one real root (repeated root).
  • If $b^2 - 4ac < 0$, there are two complex roots.

Would you like further details or a step-by-step example?

Here are 5 related questions:

1. How do you solve a quadratic equation using the quadratic formula?
2. What does the discriminant tell us about the solutions of the quadratic equation?
3. Can the quadratic formula be used if the equation isn't in standard form?
4. How do you derive the quadratic formula from completing the square?
5. What are some real-life applications of quadratic equations?

Tip: Always check the value of the discriminant first to understand the nature of the solutions.