Question 967191
The graph is either entirely above or entirely below the x-axis.  Seeing that the coefficient of the leading term is a POSITIVE 3,  the graph has a vertex at the minimum and opens upward.  This logically means that the graph is above the x-axis everywhere.  (As long as the correct value is found for c).


You want the discriminant to be less than 0 for {{{3x^2-9x+c-2.25>0}}}.
That means  {{{(-9)^2-4*3*(c-2.25)<0}}}.  Find the solution inequality for c.