Question

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

Answer 1

`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)`.