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

##### 1 Answer

Aug 3, 2017

#### 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]}