Answer
$(2,4)$
Work Step by Step
To find the vertex, the given function, $
f(x)=-3x^2+12x-8
,$ should be converted in the form $f(x)=a(x-h)^2+k$.
Grouping the variables together and making the coefficient of $x^2$ equal to $1$, the given function is equivalent to
\begin{align*}
f(x)&=(-3x^2+12x)-8
\\
f(x)&=-3(x^2-4x)-8
.\end{align*}
Completing the square of the expression with variables by adding $\left(\dfrac{b}{2}\right)^2,$ the expression above is equivalent to
\begin{align*}
f(x)&=-3\left(x^2-4x+\left(\dfrac{-4}{2}\right)^2\right)+\left[-8-(-3)\left(\dfrac{-4}{2}\right)^2\right]
\\\\
f(x)&=-3\left(x^2-4x+4\right)+\left[-8+12\right]
\\\\
f(x)&=-3\left(x-2\right)^2+4
.\end{align*}Note that $\left[a\left(\dfrac{b}{2}\right)^2\right]$ should be subtracted as well to negate the addition of that value when completing the square of the expression with variables.
Since the vertex of the quadratic function $f(x)=a(x-h)^2+k$ is given by $(h,k)$, then the vertex of the quadratic function above is $
(2,4)
$.
