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.

Discover how to solve quadratic equations using the quadratic formula ax^2 + bx + c = 0. Understand the discriminant and different scenarios for real and complex solutions. Perfect for students studying algebra and quadratic equations in Grades 7-9.

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