What is the vertex form of # f(x) = -x^2 + 3x-2 #?

1 Answer
Jul 24, 2016

#f(x)=-x^2 +3x-2=(-x+1)(x-2)#

Explanation:

#f(x)=-x^2 +3x-2=(-x+1)(x-2)# You can use foil to check that it's correct.
Let #f(x)=ax^2 +bx+c#
My thought process behind this, was:
Since in #ax^2# #a# is a negative value, one of the factors will have to be negative when using foil.
Same goes for #c#
Finally, since #b# was positive, that means that I have to arrange the #bx# and #c# in a manner that will get me a positive, i.e. #(-x)\times(-y)=+(xy)#.