# How do you find a polynomial function that has zeros 2, -6?

Jan 3, 2017

$f \left(x\right) = {x}^{2} + 4 x - 12$

#### Explanation:

The zeros are $2$ and $- 6$

Reverse their signs, you will get

$- 2$ and $6$

$\left(x - 2\right)$ and $\left(x + 6\right)$ will be a factor of the polynomial function

$f \left(x\right) = \left(x - 2\right) \left(x + 6\right)$

Multiply the two expressions

$f \left(x\right) = {x}^{2} + 6 x - 2 x - 12$

Combine like terms

$f \left(x\right) = {x}^{2} + 4 x - 12$