# What is the vertex form of  f(x) = -3x^2 + 6x -2 ?

Dec 19, 2015

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

#### Explanation:

Proceed as follows

Factor out $- 3$ from the terms with ${x}^{2}$ and $x$

$- 3 \left({x}^{2} - 2 x\right) - 2$

Now complete the square for ${x}^{2} - 2 x$

Remember when we redistribute the negative $3$ into whats in the
parentheses it is minus $3$ so we must add $3$ to maintain the original equation.

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

Factor whats in the parentheses and combine like terms

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