Answer
See graph
Work Step by Step
We are given the parabola:
$y=-3(x-1)^2+2$
Bring the equation to the standard form:
$(x-h)^2=4p(y-k)$
$3(x-1)^2=-y+2$
$(x-1)^2=-\dfrac{1}{3}(y-2)$
Determine $h,k,p$:
$h=1$
$k=2$
$4p=\dfrac{1}{3}\Rightarrow p=\dfrac{1}{12}$
Determine the vertex:
$V(h,k)=(1,2)$
Consider another points to help graphing the parabola:
$x=0\Rightarrow y=-3(0-1)^2+2=-1$
$x=2\Rightarrow y=-3(2-1)^2+2=-1$
Plot the vertex and the additional points and sketch the parabola:
