How to Use the Quadratic Formula

Understanding the Basics

The quadratic formula is a powerful tool used to solve quadratic equations – these are equations involving a variable squared, such as x2 (“quad” meaning square), and no higher power. Generally, the problems you encounter will be in standard form $ax^2 + bx + c = 0.$

The solution(s) you get will be the roots, or x-intercepts of the graphed function which will be a parabola. The quadratic formula is as follows:

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

When To Use the Quadratic Formula?

Whenever you see the words “solve for x” in a problem or “find the roots,” the quadratic formula is an option that you can use. For example, take the function $$y=2x^2-5x-3$$ with the problem asking you to find the roots. From the equation, $a=2, b=-5,$ and $c=-3.$

Plugging these into the quadratic formula,




$$x=\frac{5\pm 7}{4}$$


These are the two solutions. As an aside, these roots will the cross the x-axis at the points $(3,0)$ and $(-\frac{1}{2},0).$

And there you have it! The quadratic formula is not the only way to solve a quadratic equation – the other methods are factoring and completing the square leading into the square roots method, alternative ways to be discussed in a later blog post.

Extra Practice

For extra practice on using the quadratic formula, try out these worksheets with the answer key included.

Worksheet 1

Worksheet 2

Worksheet 3

Quadratic functions and parabolas