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

Jul 24, 2016

$f \left(x\right) = - {x}^{2} + 3 x - 2 = \left(- x + 1\right) \left(x - 2\right)$

#### Explanation:

$f \left(x\right) = - {x}^{2} + 3 x - 2 = \left(- x + 1\right) \left(x - 2\right)$ You can use foil to check that it's correct.
Let $f \left(x\right) = a {x}^{2} + b x + c$
My thought process behind this, was:
Since in $a {x}^{2}$ $a$ 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 $b x$ and $c$ in a manner that will get me a positive, i.e. $\left(- x\right) \setminus \times \left(- y\right) = + \left(x y\right)$.