# What do the variables in the quadratic formula mean?

Nov 3, 2014

The quadratic formula uses the coefficients of the quadratic equation in standard form when it is equal to zero (y = 0). A quadratic equation in standard form looks like $y = a {x}^{2} + b x + c$. The quadratic formula is $x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$, when y = 0.

Here is an example of how the coefficients of the quadratic equation are used as variables in the quadratic formula:

$0 = 2 {x}^{2} + 5 x + 3$
This means a = 2, b = 5, and c = 3.

So the quadratic formula becomes:
$x = \frac{- 5 \pm \sqrt{{5}^{2} - 4 \left(2\right) \left(3\right)}}{2 \cdot 2}$

$x = \frac{- 5 \pm \sqrt{25 - 4 \left(2\right) \left(3\right)}}{2 \cdot 2}$

$x = \frac{- 5 \pm \sqrt{25 - 24}}{2 \cdot 2}$

$x = \frac{- 5 \pm \sqrt{1}}{2 \cdot 2}$

$x = \frac{- 5 \pm 1}{2 \cdot 2}$

$x = \frac{- 5 \pm 1}{4}$

$x = \frac{- 5 + 1}{4}$ and $x = \frac{- 5 - 1}{4}$

$x = - \frac{4}{4} \mathmr{and} x = - \frac{6}{4}$

$x = - 1 \mathmr{and} x = - \frac{3}{2}$