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,
$$x=\frac{-(-5)\pm\sqrt{(-5)^2-4(2)(-3)}}{2(2)}$$
$$x=\frac{5\pm\sqrt{25+24}}{4}$$
$$x=\frac{5\pm\sqrt{49}}{4}$$
$$x=\frac{5\pm 7}{4}$$
$$x=3,-\frac{1}{2}$$
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.
Yuki is a skilled educator with a degree in Chemistry from Carnegie Mellon University. She discovered her passion for teaching math after tutoring at an after-school program. With five years of tutoring experience, Yuki creates a supportive learning environment for students. Outside of tutoring, she enjoys trying new cuisines and playing piano.
