Answer
The vertex is labeled with its coordinates, and the green line is the axis of symmetry.
Work Step by Step
$f(x)=-3(x-1)^2+1$
$f(x)=-3(x-1)(x-1)+1$
$f(x)=-3(x^2-2x+1)+1$
$f(x)=-3x^2+6x-3+1$
$f(x)=-3x^2+6x-2$
$a=-3$, $b=6$, $c=-2$
The axis of symmetry is at $x=-b/2a$
$x=-b/2a$
$x=-6/2*-3$
$x=-6/-6$
$x=1$
The vertex is at $x=1$
$f(x)=-3(x-1)^2+1$
$f(1)=-3(1-1)^2+1$
$f(1)=-3(0)^2+1$
$f(1)=-3*0+1$
$f(1)=0+1$
$f(1)=1$
$(1,1)$ is the vertex.
