Quadratic formula

The quadratic formula is a formula used to solve quadratic equations. It is the solution to the general quadratic equation. Quadratics are polynomials whose highest power term has a degree of 2.

General quadratic equation:

Quadratic formula:

a, b and c are constants, where a cannot equal 0. The ± indicates that the quadratic formula has two solutions. Each of these is referred to as a root. Geometrically, these roots represent the points at which a parabola crosses the x-axis. Thus, the quadratic formula can be used to determine the zeros of any parabola, as well as give the axis of symmetry of the parabola.

If a quadratic is missing either the bx or c term, then set b or c equal to 0. If the quadratic does not contain the ax2 term, you cannot use the quadratic formula because the denominator of the quadratic formula will equal 0. In that case, you can use algebra to find the zeros.


Using the quadratic equation


The quadratic formula mainly involves plugging numbers into the equation, but there are a few things you need to know. The part of the formula within the radical is called the discriminant:

b2 - 4ac

The discriminant tells us how many solutions the quadratic has.

In addition, notice the ± symbol. This means that when the discriminant is positive, the quadratic will have two solutions - one where you add the square root of the discriminant, and one where you subtract it.

Below is an example of using the quadratic formula:

Example


Remembering the quadratic equation


Although the quadratic equation may at first seem daunting to remember, repeated use can help. If you know the tune to "Pop goes the weasel," you can also sing the quadratic equation to its tune to help you remember the quadratic equation. The song goes:

"x is equal to negative b, plus or minus the square root, of b squared minus 4ac all over 2a."

If you're unsure how the song goes, there are numerous examples on YouTube that can help!


See also quadratic function, discriminant.