Answer
It's a parabola
vertex = $(1,-1)$
Work Step by Step
$y=-2x^2+4x−3$
Completing square and writing in vertex form $y=a(x−h)^2+k$,
$y=-2(x−1)^2−1$
The graph is a parabola and its opening down.
vertex : $(k;h)$
=$(−5;−2)$
the graph is shown below
