Question

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

Answer 1

`y=-x^2+x+6`

Explanation:

`"since the zeros(roots) are "x=-2" and "x=3`

`"then the factors are"`

`x+2)(x-3)`

`rArry=(x+2)(x-3)`

`rArry=x^2-x-6`

`"for the condition that "yto-oo" as "xto-oo`

`"we require the coefficient of "x^2" to be negative"`

`rArry=-(x^2-x-6)`

`color(white)(rArry)=-x^2+x+6" is the required polynomial"`
graph{-x^2+x+6 [-20, 20, -10, 10]}