for these problems you want to graph the parabola y=ax^2 +bx +c
It will U shaped if a>0 and upside down U shaped if a<0
if it is < or > rather than <= or >= then the graph is dotted to indicate that the parabola itself is not part of the solution
you will then be shading in either below or above the parabola
checking whether (0,0) is part of the solution or not ; it is an easy check whether you have shaded the correct region
for y>3x^2-8x
y>x(3x-8)
the graph crosses the x-axis at (0,) and (8/3,0); it is U shaped
you can plot a few more points for accuracy, dot in the parabola, shade above
same for y>x^2-5x =x(x-5)
goes through (0,0) and (5.0), vertex (bottom of graph is (2.5, -6.25)
dotted line, U-shaped, shade above
the third graph is an inverted U, dotted, shade inside and below the parabola
-(6x^2 -2x-3) this doesn't factor so plot some points