# What does b stand for in quadratic function?

Jun 1, 2015

$b$ conventionally stands for the coefficient of the middle term of a quadratic expression.

The normal form of a generic quadratic equation in one variable $x$ is:

$a {x}^{2} + b x + c = 0$

Associated with such a quadratic equation is the discriminant $\Delta$ given by the formula:

$\Delta = {b}^{2} - 4 a c$

The general solution of the quadratic equation may be written

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

or

$x = \frac{- b \pm \sqrt{\Delta}}{2 a}$

Often people will assume that $a$ is understood to be the coefficient of ${x}^{2}$, $b$ the coefficient of $x$ and $c$ the constant term, and they will proceed directly from a quadratic equation such as $2 {x}^{2} - 3 x + 1 = 0$ to speaking of something like ${b}^{2} - 4 a c$ without telling you that $a = 2$, $b = - 3$ and $c = 1$ are the coefficients.