# What is an example of using the quadratic formula?

##### 1 Answer

Suppose that you have a function represented by

We can use the quadratic formula to find the zeroes of this function, by setting

Technically we can also find complex roots for it, but typically one will be asked to work only with real roots. The quadratic formula is represented as:

#(-B +- sqrt(B^2-4AC))/(2A) = x#

... where x represents the x-coordinate of the zero.

If

As an example, consider the function

#A = 1, B = -13, C = 12.#

Then for the quadratic formula we would have:

# x = (13 +- sqrt ((-13)^2 - 4(1)(12)))/(2(1))# =

#(13 +- sqrt (169 - 48))/2 = (13+-11)/2#

Thus, our roots are

For an example with complex roots, we have the function

Then by the quadratic equation,

#x = (0 +- sqrt (0^2 - 4(1)(1)))/(2(1)) = +-sqrt(-4)/2 = +-i#

... where

In the graph for this function on the real coordinate plane, we will see no zeroes, but the function will have these two imaginary roots.