The Quadratic Formula: Definition and Applications!

Quadratic Formula
Quadratic Formula

The quadratic formula is an essential tool in solving quadratic equations. Every student who has taken a high school math course has learned this formula, but not all students fully understand it. Quadratic equations are a fundamental part of algebra and are used to solve various real-world problems.

Keep reading to explore the quadratic formula, step-by-step, including how and why the quadratic formula is used. If you wonder how to prove that three points are collinear, I wrote a whole article discussing 4 Different methods to prove that three points are collinear.

What Is The Quadratic Formula?

The quadratic formula is a formula that gives the solutions to quadratic equations of the form ax² + bx + c = 0. The coefficients a, b, and c represent the constants in the quadratic equation.

The quadratic formula is expressed as x = (-b ± √(b²-4ac))/(2a). It is essential to note that the discriminant (b²-4ac) determines the nature of the solution to the quadratic equation.

Using The Quadratic Formula to Solve Quadratic Equations

Using the quadratic formula to solve quadratic equations involves plugging in the values of the coefficients (a, b, and c) into the formula and simplifying the expression.

The quadratic formula is used to solve for the values of x that make the equation true. The formula is x = (-b ± √(b² – 4ac))/(2a).

  • The first step in using the quadratic formula is to identify the values of a, b, and c from the quadratic equation. Once you have identified these values, you can substitute them into the formula.
  • Next, you need to simplify the equation by simplifying the square root portion of the formula. Remember:
    • If the discriminant, which is b² – 4ac, is negative, then the quadratic equation has no real solutions (But there are two complex solutions)
    • If the discriminant is positive, there are two real solutions.
    • If it is zero, there is one repeated real solution.

Also, remember that the quadratic formula works for every quadratic equation, regardless of the values of a, b, and c. However, sometimes a quadratic equation can be solved more simply by factoring or completing the square.

I encourage you to watch this video or the video below and check out Khan Academy for more practice questions on the quadratic formula.

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Wrapping Up

The quadratic formula is a useful tool for solving quadratic equations. Remember first to identify the values of a, b, and c, then substitute them into the formula, simplify the equation, and finally solve for x.

In essence, learning the quadratic formula is critical in the study of algebra and calculus, and mathematics in general.


I am Altiné. I am the guy behind When I am not teaching math, you can find me reading, running, biking, or doing anything that allows me to enjoy nature's beauty. I hope you find what you are looking for while visiting

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