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

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Answer 1 · 2015-12-19T19:13:40

$-3(x-1)^2+1$

Proceed as follows

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

$-3(x^2-2x)-2$

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

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.

$-3(x^2-2x+1)-2+3$

Factor whats in the parentheses and combine like terms

$-3(x-1)^2+1$

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