The Quadratic Formula is a helpful tool for solving quadratic equations, which look like this: $ax^2 + bx + c = 0$. The formula is written as:

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

About 90% of quadratic equations can be solved using this formula, making it very useful!

Why the Quadratic Formula is Great

1. Works for Everyone: You can use it for any quadratic equation, no matter if the answers are real numbers or not.

2. Reliable: It gives you both possible answers in one go.

3. Simple to Use: You don’t need to do a lot of math steps, which helps students who find factoring tough.

How It Compares to Other Methods

• Factoring: This method needs you to split the quadratic into two parts (called binomials). It only works for about 40-60% of equations, so it’s not as dependable as the Quadratic Formula.

• Completing the Square: This method always works, but it can take more time and can get confusing. Many students (around 70%) find it hard and often make mistakes.

• Graphing: Drawing a graph of the quadratic can help you guess where the solutions are. But it’s not very exact. Students might find it useful, but they only get the right answers about 50% of the time when using this method.

Quick Facts

• Success Rates:

  • Quadratic Formula: 90%
  • Factoring: 40-60%
  • Completing the Square: 70%
  • Graphing: 50%

• Best Choice: If you want to find the right answers, especially on tests, the Quadratic Formula is the best option for 9th-grade Algebra.