Graph #y = -2x^2-x+3 #.
The graph is a parabola.
We could graph this by finding the vertex and so on, but I find it simpler to just find the #x# intercepts
#-2x^2-x+3 - -(2x^2+x-3) = -(2xcolor(white)"XXX")(xcolor(white)"XXX")#
# = -(2x+3)(x-1)#
So the #x# intercepts are #-3/2# and #1#.
The #y# intercept is #3#, so the graph of the equation is
graph{ -2x^2-x+3 [-8.62, 7.186, -3.96, 3.94]}
Testing #(0,0)# we see that #0 >= -2(0)^2-(0)+3# is false so there are no solutions in the region containing the origin.
Testing #(0,5)# (remember the #y# intercept is #3#) or #(1,3)# or #(5,0)# or some other point outside the region containing #(0,0)#, we learn the the region not containing #(0,0)# contains the solutions
OR We can reason the the values of #y# greater than -2x^2-x+3 are above the curve.
graph{y >= -2x^2-x+3 [-8.62, 7.186, -3.96, 3.94]} .
