# How do you write a second-degree polynomial, with zeros of -2 and 3, and goes to -oo as x->-oo?

Aug 3, 2017

$y = - {x}^{2} + x + 6$

#### Explanation:

$\text{since the zeros(roots) are "x=-2" and } x = 3$

$\text{then the factors are}$

x+2)(x-3)

$\Rightarrow y = \left(x + 2\right) \left(x - 3\right)$

$\Rightarrow y = {x}^{2} - x - 6$

$\text{for the condition that "yto-oo" as } x \to - \infty$

$\text{we require the coefficient of "x^2" to be negative}$

$\Rightarrow y = - \left({x}^{2} - x - 6\right)$

$\textcolor{w h i t e}{\Rightarrow y} = - {x}^{2} + x + 6 \text{ is the required polynomial}$
graph{-x^2+x+6 [-20, 20, -10, 10]}