Question 458034
Since a=-2 the parabola opens down. We know that the coordinates of vertex is the point: (x=-b/2a=-3/-4=3/4, and y=f(3/4)=-2*(3/4)^2+3*3/4+2=25/8), (3/4, 25/8)

Since {{{-2x^2+3x+2=(2x+1)(2-x)}}}, the graph intersect the x-axis at x=2 and 

x=-1/2.

See the graph below:

{{{graph(300, 300, -5, 5, -5, 5, -2x^2+3x+2)}}}.